Duan Wu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Duan Wu has a total of 1 co-authors. Here are the top co-authors by number of shared publications:
- Michael Winkler
Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
1 shared publication
Latest Publications
- 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
Refined existence theorems for doubly degenerate chemotaxis-consumption systems with large initial data
This work considers the doubly degenerate nutrient model \begin{equation*}\label{AH1} \left\{ \begin{split} &u_t=\nabla\cdot\left(u^{m-1}v\nabla u\right)-\nabla\cdot\left(f(u)v\nabla v\right)+\ell uv,&&x\inΩ,\,t>0, &v_t=Δv-uv, &&x\inΩ,\,t>0, \end{split} \right. \end{equation*} under no-flux boundary conditions in a smoothly bounded convex domain $Ω\subset \mathbb{R}^n$ ($n\le 2$), where the nonnegative function $f\in C^1([0,\infty))$ is assumed to satisfy $f(s)\le C_fs^α$ with $α>0$ and $C_f>0$ for all $s\ge 1$. When $m=2$, it was shown that a global weak solution exists, either in one-dimensional setting with $α=2$, or in two-dimensional version with $α\in(1,\frac{3}{2})$. The main results in this paper assert the global existence of weak solutions for $1\le m<3$ and classical solutions for $3\le m<4$ to the above system under the assumption \begin{equation*} α\in \left\{ \begin{split} &\left[m-1,\min\left\{m,\frac{m}{2}+1\right\}\right]~~&&\textrm{if}~~n=1,\quad\quad\textrm{and} &\left(m-1,\min\left\{m,\frac{m}{2}+1\right\}\right)~~&&\textrm{if}~~n=2, \end{split} \right. \end{equation*} which extend the range $α\in(1,\frac{3}{2})$ to $α\in(1,2)$ in two dimensions for the case $m=2$. Our proof will be based on a new observation on the coupled energy-type functional and on an inequality with general form.Open AccessRefined existence theorems for doubly degenerate chemotaxis-consumption systems with large initial data
This work considers the doubly degenerate nutrient model \begin{equation*}\label{AH1} \left\{ \begin{split} &u_t=\nabla\cdot\left(u^{m-1}v\nabla u\right)-\nabla\cdot\left(f(u)v\nabla v\right)+\ell uv,&&x\inΩ,\,t>0, &v_t=Δv-uv, &&x\inΩ,\,t>0, \end{split} \right. \end{equation*} under no-flux boundary conditions in a smoothly bounded convex domain $Ω\subset \mathbb{R}^n$ ($n\le 2$), where the nonnegative function $f\in C^1([0,\infty))$ is assumed to satisfy $f(s)\le C_fs^α$ with $α>0$ and $C_f>0$ for all $s\ge 1$. When $m=2$, it was shown that a global weak solution exists, either in one-dimensional setting with $α=2$, or in two-dimensional version with $α\in(1,\frac{3}{2})$. The main results in this paper assert the global existence of weak solutions for $1\le m<3$ and classical solutions for $3\le m<4$ to the above system under the assumption \begin{equation*} α\in \left\{ \begin{split} &\left[m-1,\min\left\{m,\frac{m}{2}+1\right\}\right]~~&&\textrm{if}~~n=1,\quad\quad\textrm{and} &\left(m-1,\min\left\{m,\frac{m}{2}+1\right\}\right)~~&&\textrm{if}~~n=2, \end{split} \right. \end{equation*} which extend the range $α\in(1,\frac{3}{2})$ to $α\in(1,2)$ in two dimensions for the case $m=2$. Our proof will be based on a new observation on the coupled energy-type functional and on an inequality with general form.