Michael Winkler
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The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
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Michael Winkler has a total of 46 co-authors. Here are the top co-authors by number of shared publications:
- Youshan Tao
School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China
14 shared publications - Johannes Lankeit
Leibniz Universität Hannover, Institut für Angewandte Mathematik, 30167 Hannover, Germany
10 shared publications - Youshan Tao
Department of Applied Mathematics, Dong Hua University, Shanghai 200051, China
6 shared publications - Yulan Wang
School of Science, Xihua University, Chengdu, China
6 shared publications - Christina Surulescu
Department of Mathematics RPTU Kaiserslautern-Landau Gottlieb-Daimler-Str. 48 67663 Kaiserslautern Germany
5 shared publications - Marek Fila
Department of Applied Mathematics and Statistics, Comenius University, Bratislava, Slovakia
5 shared publications
Latest Publications
- Open Access
- 1 January 2027
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 58, 164-178
Bounded solutions in three-dimensional cross-degenerate nutrient-taxis systems
In a smoothly bounded domain $ \Omega \subset \mathbb{R}^n $, $ n\le 3 $, we consider the Neumann initial-boundary problem for the cross-degenerate chemotaxis-consumption system $ \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \nabla \cdot (u^ \alpha v\nabla u) - \chi \nabla\cdot (u^{ \alpha+1} v\nabla v) + \ell uv, \\ v_t = \Delta v - uv, \end{array} \right. \qquad \qquad (\star) \end{eqnarray*} $ with $ \alpha\ge 0 $, which was proposed in [Nature 578, 588-592 (2020)] for $ \alpha = 0 $ to explore the role of motility in boosting bacterial diversity, and in [Physica A 392, 5644-5662 (2013)] for $ \alpha = 1 $ to explain the formation of complex patterns in populations of bacteria in nutrient-poor environments. It is shown that for any given suitably regular initial data $ (u_0, v_0) $ with $ u_0\ge 0 $ and $ v_0>0 $, there exists $ \delta = \delta(u_0, v_0, \alpha)>0 $ such that whenever $ \chi\in [0, \delta] $ and $ \ell\in [0, \delta] $, the problem admits a global bounded solution, weak in the case when $ \alpha>0 $ and classical if $ \alpha = 0 $.- 1 January 2027
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 58, 164-178
Open AccessBounded solutions in three-dimensional cross-degenerate nutrient-taxis systems
In a smoothly bounded domain $ \Omega \subset \mathbb{R}^n $, $ n\le 3 $, we consider the Neumann initial-boundary problem for the cross-degenerate chemotaxis-consumption system $ \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \nabla \cdot (u^ \alpha v\nabla u) - \chi \nabla\cdot (u^{ \alpha+1} v\nabla v) + \ell uv, \\ v_t = \Delta v - uv, \end{array} \right. \qquad \qquad (\star) \end{eqnarray*} $ with $ \alpha\ge 0 $, which was proposed in [Nature 578, 588-592 (2020)] for $ \alpha = 0 $ to explore the role of motility in boosting bacterial diversity, and in [Physica A 392, 5644-5662 (2013)] for $ \alpha = 1 $ to explain the formation of complex patterns in populations of bacteria in nutrient-poor environments. It is shown that for any given suitably regular initial data $ (u_0, v_0) $ with $ u_0\ge 0 $ and $ v_0>0 $, there exists $ \delta = \delta(u_0, v_0, \alpha)>0 $ such that whenever $ \chi\in [0, \delta] $ and $ \ell\in [0, \delta] $, the problem admits a global bounded solution, weak in the case when $ \alpha>0 $ and classical if $ \alpha = 0 $. - Open Access
- 6 August 2026
- Published by IOP Publishing in Nonlinearity
- Vol. 39 (8) , 085010
Bounded small-signal solutions in a three-dimensional doubly degenerate chemotaxis system
A no-flux initial-boundary value problem for { l u t = ∇ ⋅ ( u v ∇ u ) − χ ∇ ⋅ ( u 2 v ∇ v ) + ℓ u v , v t = Δ v − u v , ( ⋆ ) is considered in a smoothly bounded and not necessarily convex domain Ω ⊂ R n with n ⩽ 3 , with nonnegative parameters χ and ℓ , and under the initial condition ( u , v ) | t = 0 = ( u 0 , v 0 ) with given functions u 0 and v 0 from W 1 , ∞ ( Ω ) which satisfy u 0 ⩾ 0 , u 0 ≢ 0 , and v 0 > 0 in Ω ― . It is seen that under an appropriate smallness assumption on v 0 , a global bounded weak solution exists which approaches a nontrivial equilibrium ( u ∞ , 0 ) in the large time limit. This is achieved by means of a Moser iteration involving an apparently novel class of functional inequalities, arranged along with a regularity analysis of signal gradients in a loop-type manner. The estimates gained in the course of this are finally used to indicate that two fundamental dynamical properties known from one-dimensional situations indeed extend to arbitrary domains of physical relevance: It is shown, namely, that if u 0 is not constant and v 0 is subject to a possibly strengthened smallness assumption, then u ∞ ≢ c o n s t . , and a stability property of each of the states ( u ⋆ , 0 ) , with arbitrary nonnegative and nontrivial u ⋆ ∈ W 1 , ∞ ( Ω ) , is identified.
- 6 August 2026
- Published by IOP Publishing in Nonlinearity
- Vol. 39 (8) , 085010
Open AccessBounded small-signal solutions in a three-dimensional doubly degenerate chemotaxis system
A no-flux initial-boundary value problem for { l u t = ∇ ⋅ ( u v ∇ u ) − χ ∇ ⋅ ( u 2 v ∇ v ) + ℓ u v , v t = Δ v − u v , ( ⋆ ) is considered in a smoothly bounded and not necessarily convex domain Ω ⊂ R n with n ⩽ 3 , with nonnegative parameters χ and ℓ , and under the initial condition ( u , v ) | t = 0 = ( u 0 , v 0 ) with given functions u 0 and v 0 from W 1 , ∞ ( Ω ) which satisfy u 0 ⩾ 0 , u 0 ≢ 0 , and v 0 > 0 in Ω ― . It is seen that under an appropriate smallness assumption on v 0 , a global bounded weak solution exists which approaches a nontrivial equilibrium ( u ∞ , 0 ) in the large time limit. This is achieved by means of a Moser iteration involving an apparently novel class of functional inequalities, arranged along with a regularity analysis of signal gradients in a loop-type manner. The estimates gained in the course of this are finally used to indicate that two fundamental dynamical properties known from one-dimensional situations indeed extend to arbitrary domains of physical relevance: It is shown, namely, that if u 0 is not constant and v 0 is subject to a possibly strengthened smallness assumption, then u ∞ ≢ c o n s t . , and a stability property of each of the states ( u ⋆ , 0 ) , with arbitrary nonnegative and nontrivial u ⋆ ∈ W 1 , ∞ ( Ω ) , is identified.
- Open Access
Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid
This manuscript is concerned with the one-dimensional system \[ \begin{array}{l} τu_{ttt} + αu_{tt} = b \big(γ(Θ) u_{xt}\big)_x + \big( γ(Θ) u_x\big)_x, \\[1mm] Θ_t = D Θ_{xx} + bγ(Θ) u_{xt}^2, \end{array} \] which is connected to the simplified modeling of heat generation in Zener type materials subject to stress from acoustic waves. Under the assumption that the coefficients $τ>0, b>0$ and $α\geq0$ satisfy \begin{align}\tag{$\star$} αb >τ, \end{align} it is shown that for all $Θ_\star>0$ one can find $ν=ν(D,τ,α,b,Θ_\star,γ)>0$ such that an associated Neumann type initial-boundary value problem with Neumann data admits a unique time-global solution in a suitable framework of strong solvability whenever the initial temperature distribution fulfills $$\|Θ_0\|_{L^\infty(Ω)}\leq Θ_\star$$ and the derivatives of the initial data are sufficiently small in the sense of satisfying $$\int_Ωu_{0xx}^2 + \int_Ω(u_{0t})_{xx}^2 + \int_Ω(u_{0tt})_x^2 < ν\quad\text{and}\quad \|Θ_{0x}\|_{L^\infty(Ω)} + \|Θ_{0xx}\|_{L^\infty(Ω)} < ν.$$ The constructed solution moreover features an exponential stabilization property for both components. In particular, the parameter range described by ($\star$) coincides with the full stability regime known for the corresponding Moore--Gibson--Thompson equation despite the fairly strong nonlinear coupling to the temperature variable.Open AccessGlobal solutions and large time stabilization in a model for thermoacoustics in a standard linear solid
This manuscript is concerned with the one-dimensional system \[ \begin{array}{l} τu_{ttt} + αu_{tt} = b \big(γ(Θ) u_{xt}\big)_x + \big( γ(Θ) u_x\big)_x, \\[1mm] Θ_t = D Θ_{xx} + bγ(Θ) u_{xt}^2, \end{array} \] which is connected to the simplified modeling of heat generation in Zener type materials subject to stress from acoustic waves. Under the assumption that the coefficients $τ>0, b>0$ and $α\geq0$ satisfy \begin{align}\tag{$\star$} αb >τ, \end{align} it is shown that for all $Θ_\star>0$ one can find $ν=ν(D,τ,α,b,Θ_\star,γ)>0$ such that an associated Neumann type initial-boundary value problem with Neumann data admits a unique time-global solution in a suitable framework of strong solvability whenever the initial temperature distribution fulfills $$\|Θ_0\|_{L^\infty(Ω)}\leq Θ_\star$$ and the derivatives of the initial data are sufficiently small in the sense of satisfying $$\int_Ωu_{0xx}^2 + \int_Ω(u_{0t})_{xx}^2 + \int_Ω(u_{0tt})_x^2 < ν\quad\text{and}\quad \|Θ_{0x}\|_{L^\infty(Ω)} + \|Θ_{0xx}\|_{L^\infty(Ω)} < ν.$$ The constructed solution moreover features an exponential stabilization property for both components. In particular, the parameter range described by ($\star$) coincides with the full stability regime known for the corresponding Moore--Gibson--Thompson equation despite the fairly strong nonlinear coupling to the temperature variable. - Open Access
Large time stabilization of rough-data solutions in one-dimensional nonlinear thermoelasticity
In an open bounded real interval $Ω$, the model for one-dimensional thermoelasticity given by \[ u_{tt} = u_{xx} - \big(f(Θ)\big)_x, \qquad Θ_t = Θ_{xx} - f(Θ) u_{xt}, \] is considered along with homogeneous boundary conditions of Dirichlet type for $u$ and of Neumann type for $Θ$, under the assumption that $f\in C^1([0,\infty))$ satisfies $f(0)=0$, $f'\in L^\infty((0,\infty))$ and $f'>0$ on $[0,\infty)$. The focus is on initial data which are merely required to be consistent with the fundamental principles of energy conservation and entropy nondecrease, by satisfying \[ u_0\in W_0^{1,2}(Ω), u_{0t} \in L^2(Ω), 0 \le Θ_0\in L^1(Ω), Θ_0 \not\equiv 0. \] Despite an apparent lack of favorable compactness properties that have underlain previous related studies on more regular settings, it is shown that corresponding weak solutions stabilize in the sense that \[ \lim_{t\to\infty} \|u(\cdot,t)\|_{L^\infty(Ω)}=0 \] and \[ {\rm ess} \lim_{\!\!\!\! t\to\infty} \|Θ(\cdot,t)-Θ_\infty\|_{L^\infty(Ω)}=0 \] with some $Θ_\infty>0$.Open AccessLarge time stabilization of rough-data solutions in one-dimensional nonlinear thermoelasticity
In an open bounded real interval $Ω$, the model for one-dimensional thermoelasticity given by \[ u_{tt} = u_{xx} - \big(f(Θ)\big)_x, \qquad Θ_t = Θ_{xx} - f(Θ) u_{xt}, \] is considered along with homogeneous boundary conditions of Dirichlet type for $u$ and of Neumann type for $Θ$, under the assumption that $f\in C^1([0,\infty))$ satisfies $f(0)=0$, $f'\in L^\infty((0,\infty))$ and $f'>0$ on $[0,\infty)$. The focus is on initial data which are merely required to be consistent with the fundamental principles of energy conservation and entropy nondecrease, by satisfying \[ u_0\in W_0^{1,2}(Ω), u_{0t} \in L^2(Ω), 0 \le Θ_0\in L^1(Ω), Θ_0 \not\equiv 0. \] Despite an apparent lack of favorable compactness properties that have underlain previous related studies on more regular settings, it is shown that corresponding weak solutions stabilize in the sense that \[ \lim_{t\to\infty} \|u(\cdot,t)\|_{L^\infty(Ω)}=0 \] and \[ {\rm ess} \lim_{\!\!\!\! t\to\infty} \|Θ(\cdot,t)-Θ_\infty\|_{L^\infty(Ω)}=0 \] with some $Θ_\infty>0$. - Open Access
A simple model for one-dimensional nonlinear thermoelasticity: Well-posedness in rough-data frameworks
In an open bounded interval $Ω$, the problem \[ u_{tt} = u_{xx} - \big(f(Θ)\big)_x, Θ_t = Θ_{xx} - f(Θ) u_{xt}, \] is considered under the boundary conditions $u|_{\partialΩ}=Θ_x|_{\partialΩ}=0$, and for $f\in C^2([0,\infty))$ satisfying $f(0)=0$, $f'>0$ on $[0,\infty)$ and $f'\in W^{1,\infty}((0,\infty))$. In the sense of unconditional global existence, uniqueness and continuous dependence, this problem is shown to be well-posed within ranges of initial data merely satisfying \[ u_0\in W_0^{1,2}(Ω), \quad u_{0t} \in L^2(Ω) \quad \mbox{and} \quad Θ_0 \in L^2(Ω) \mbox{ with $Θ\ge 0$ a.e.~in $Ω$,} \] and in classes of solutions fulfilling \[ u\in C^0([0,\infty);W_0^{1,2}(Ω)), \qquad u_t \in C^0([0,\infty);L^2(Ω)) \qquad \mbox{and} \qquad Θ\in C^0([0,\infty);L^2(Ω)) \cap L^2_{loc}([0,\infty);W^{1,2}(Ω)). \]Open AccessA simple model for one-dimensional nonlinear thermoelasticity: Well-posedness in rough-data frameworks
In an open bounded interval $Ω$, the problem \[ u_{tt} = u_{xx} - \big(f(Θ)\big)_x, Θ_t = Θ_{xx} - f(Θ) u_{xt}, \] is considered under the boundary conditions $u|_{\partialΩ}=Θ_x|_{\partialΩ}=0$, and for $f\in C^2([0,\infty))$ satisfying $f(0)=0$, $f'>0$ on $[0,\infty)$ and $f'\in W^{1,\infty}((0,\infty))$. In the sense of unconditional global existence, uniqueness and continuous dependence, this problem is shown to be well-posed within ranges of initial data merely satisfying \[ u_0\in W_0^{1,2}(Ω), \quad u_{0t} \in L^2(Ω) \quad \mbox{and} \quad Θ_0 \in L^2(Ω) \mbox{ with $Θ\ge 0$ a.e.~in $Ω$,} \] and in classes of solutions fulfilling \[ u\in C^0([0,\infty);W_0^{1,2}(Ω)), \qquad u_t \in C^0([0,\infty);L^2(Ω)) \qquad \mbox{and} \qquad Θ\in C^0([0,\infty);L^2(Ω)) \cap L^2_{loc}([0,\infty);W^{1,2}(Ω)). \] - Open Access
Global solvability and stabilization in multi-dimensional small-strain nonlinear thermoviscoelasticity
Despite considerable developments in the literature of the past decades, a standing open problem in the analysis of continuum mechanics appears to consist of determining how far the prototypical model for small-strain thermoviscoelastic evolution in Kelvin-Voigt materials with inertia, as given by \[ u_{tt} = μΔu_t + (λ+μ)\nabla\nabla\cdot u_t + \hatμ Δu + (\hatλ+\hatμ) \nabla\nabla\cdot u - B\nablaΘ, \qquad \qquad κΘ_t = DΔΘ+ μ|\nabla u_t|^2 + (λ+μ) |{\rm div} \, u_t|^2 - BΘ{\rm div} \, u_t, \qquad \qquad \qquad (\star) \] is globally solvable in multi-dimensional settings and for initial data of arbitrary size. The present manuscript addresses this in the context of an initial value problem in smoothly bounded $n$-dimensional domains with $n\ge 2$, posed under homogeneous boundary conditions of Dirichlet type for the displacement variable $u$, and of Neumann type for the temperature $Θ$. Within suitably generalized concepts of solvability, global existence of solutions is shown without any size restrictions on the data, and for a system actually more general than ($\star$) by, inter alia, allowing the heat capacity $κ$ to depend on $Θ$. Apart from that, results on large time behavior are derived which particularly assert stabilization of $Θ$ toward a spatially homogeneous limit. Besides on standard features related to energy conservation and entropy production, in its core parts the analysis relies on an evolution property of certain logarithmic refinements of classical entropy functionals, to the best of our knowledge undiscovered in precedent literature and possibly of independent interest.Open AccessGlobal solvability and stabilization in multi-dimensional small-strain nonlinear thermoviscoelasticity
Despite considerable developments in the literature of the past decades, a standing open problem in the analysis of continuum mechanics appears to consist of determining how far the prototypical model for small-strain thermoviscoelastic evolution in Kelvin-Voigt materials with inertia, as given by \[ u_{tt} = μΔu_t + (λ+μ)\nabla\nabla\cdot u_t + \hatμ Δu + (\hatλ+\hatμ) \nabla\nabla\cdot u - B\nablaΘ, \qquad \qquad κΘ_t = DΔΘ+ μ|\nabla u_t|^2 + (λ+μ) |{\rm div} \, u_t|^2 - BΘ{\rm div} \, u_t, \qquad \qquad \qquad (\star) \] is globally solvable in multi-dimensional settings and for initial data of arbitrary size. The present manuscript addresses this in the context of an initial value problem in smoothly bounded $n$-dimensional domains with $n\ge 2$, posed under homogeneous boundary conditions of Dirichlet type for the displacement variable $u$, and of Neumann type for the temperature $Θ$. Within suitably generalized concepts of solvability, global existence of solutions is shown without any size restrictions on the data, and for a system actually more general than ($\star$) by, inter alia, allowing the heat capacity $κ$ to depend on $Θ$. Apart from that, results on large time behavior are derived which particularly assert stabilization of $Θ$ toward a spatially homogeneous limit. Besides on standard features related to energy conservation and entropy production, in its core parts the analysis relies on an evolution property of certain logarithmic refinements of classical entropy functionals, to the best of our knowledge undiscovered in precedent literature and possibly of independent interest. - 5 February 2026
- Published by Springer Nature in Journal of Mathematical Fluid Mechanics
- Vol. 28 (2) , 24
$L^\infty $ Bounds Under Optimal Conditions on Integrability of Forces in the Two-dimensional Navier-Stokes System- 5 February 2026
- Published by Springer Nature in Journal of Mathematical Fluid Mechanics
- Vol. 28 (2) , 24
$L^\infty $ Bounds Under Optimal Conditions on Integrability of Forces in the Two-dimensional Navier-Stokes System- Open Access
Hotspot formation driven by temperature-dependent coefficients in one-dimensional thermoviscoelasticity
This manuscript is concerned with a two-component evolution system generalizing the classical model for one-dimensional thermoviscoelastic dynamics in Kelvin-Voigt materials in the presence of temperature-dependent viscosities and elastic stiffnesses. Under suitable assumptions on the growth of these ingredients and on the initial data, the occurrence of finite-time blow-up with respect to the $L^\infty$ norm in the temperature variable is discovered.Open AccessHotspot formation driven by temperature-dependent coefficients in one-dimensional thermoviscoelasticity
This manuscript is concerned with a two-component evolution system generalizing the classical model for one-dimensional thermoviscoelastic dynamics in Kelvin-Voigt materials in the presence of temperature-dependent viscosities and elastic stiffnesses. Under suitable assumptions on the growth of these ingredients and on the initial data, the occurrence of finite-time blow-up with respect to the $L^\infty$ norm in the temperature variable is discovered. - Open Access
Large-data global solutions to a quasilinear model for viscuos acoustic wave propagation in a non-isothermal setting
The manuscript considers the model for conversion of mechanical energy into heat during acoustic wave propagation in the presence of temperature-dependent elastic parameters, as given by \[ \left\{ \begin{array}{l} u_{tt} = (γ(Θ) u_{xt})_x + a (γ(Θ) u_x)_x, \\[1mm] Θ_t = DΘ_{xx} + γ(Θ) u_{xt}^2. \end{array} \right. \qquad \qquad (\star) \] It is firstly shown that when considered along with no-flux boundary conditions in an open bounded real interval $Ω$, under the assumption that $γ\in C^2([0,\infty))$ is such that $γ>0$ and $γ'\ge 0$ on $[0,\infty)$ as well as \[ D\cdot (γ+D) \cdot γ'' + 2γγ'^2 \le 0 \qquad \mbox{on } [0,\infty), \] for all suitably regular initial data this problem admits a globally defined classical solution. This complements recent findings in the literature, according to which ($\star$) may admit solutions blowing up in finite time whenever $γ$ is positive and nondecreasing on $[0,\infty)$ with $\int_0^\infty \frac{dξ}{γ(ξ)} < \infty$. Apart from that, it is found that if the additional assumption \[ a|Ω|^2 \le \frac{π^2 γ(0)}{1+\sqrt{1+\frac{γ(0)}{D}}} \] is satisfied, the all these solutions stabilize toward some spatially homogeneous equilibrium in the large time limit.Open AccessLarge-data global solutions to a quasilinear model for viscuos acoustic wave propagation in a non-isothermal setting
The manuscript considers the model for conversion of mechanical energy into heat during acoustic wave propagation in the presence of temperature-dependent elastic parameters, as given by \[ \left\{ \begin{array}{l} u_{tt} = (γ(Θ) u_{xt})_x + a (γ(Θ) u_x)_x, \\[1mm] Θ_t = DΘ_{xx} + γ(Θ) u_{xt}^2. \end{array} \right. \qquad \qquad (\star) \] It is firstly shown that when considered along with no-flux boundary conditions in an open bounded real interval $Ω$, under the assumption that $γ\in C^2([0,\infty))$ is such that $γ>0$ and $γ'\ge 0$ on $[0,\infty)$ as well as \[ D\cdot (γ+D) \cdot γ'' + 2γγ'^2 \le 0 \qquad \mbox{on } [0,\infty), \] for all suitably regular initial data this problem admits a globally defined classical solution. This complements recent findings in the literature, according to which ($\star$) may admit solutions blowing up in finite time whenever $γ$ is positive and nondecreasing on $[0,\infty)$ with $\int_0^\infty \frac{dξ}{γ(ξ)} < \infty$. Apart from that, it is found that if the additional assumption \[ a|Ω|^2 \le \frac{π^2 γ(0)}{1+\sqrt{1+\frac{γ(0)}{D}}} \] is satisfied, the all these solutions stabilize toward some spatially homogeneous equilibrium in the large time limit. - Open Access
Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid
This manuscript is concerned with the evolution system \[ \left\{ \begin{array}{l} u_{ttt} + αu_{tt} = \big(γ(Θ) u_{xt}\big)_x + \big( \widehatγ(Θ) u_x\big)_x, Θ_t = D Θ_{xx} + Γ(Θ) u_{xt}^2, \end{array} \right. \] which arises as a simplified model for heat generation during acoustic wave propagation in a one-dimensional viscoelastic medium of standard linear solid type. Under the assumptions that $D>0$ and $α\ge 0$, and that $γ, \widehatγ$ and $Γ$ are sufficiently smooth with $γ>0, \widehatγ>0$ and $Γ\ge 0$ on $[0,\infty)$, for suitably regular initial data a statement on local existence and uniqueness of solutions in an associated Neumann problem is derived in a suitable framework of strong solvability.Open AccessLocal strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid
This manuscript is concerned with the evolution system \[ \left\{ \begin{array}{l} u_{ttt} + αu_{tt} = \big(γ(Θ) u_{xt}\big)_x + \big( \widehatγ(Θ) u_x\big)_x, Θ_t = D Θ_{xx} + Γ(Θ) u_{xt}^2, \end{array} \right. \] which arises as a simplified model for heat generation during acoustic wave propagation in a one-dimensional viscoelastic medium of standard linear solid type. Under the assumptions that $D>0$ and $α\ge 0$, and that $γ, \widehatγ$ and $Γ$ are sufficiently smooth with $γ>0, \widehatγ>0$ and $Γ\ge 0$ on $[0,\infty)$, for suitably regular initial data a statement on local existence and uniqueness of solutions in an associated Neumann problem is derived in a suitable framework of strong solvability.