Xiongmei Fan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Xiongmei Fan has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Sen Ming
Department of Mathematics, North University of China, Taiyuan 030051, China
5 shared publications - Wei Han
North Univ China, Dept Math, Taiyuan 030051, Peoples R China
2 shared publications - Han Yang
School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China
1 shared publication - Jie Yang
Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, China
1 shared publication - Xiao Wu
Department of Mathematics, North University of China, Taiyuan 030051, China
1 shared publication Yeqin Su
Southwestern Univ Finance & Econ, Dept Secur & Futures, Liutai Rd, Chengdu 611130, Peoples R China
1 shared publication
Latest Publications
- 1 January 2027
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 17 (2) , 1232-1252
BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS
This article is devoted to investigating the initial boundary value problem of semilinear viscous Moore-Gibson-Thompson equation with general initial values and nonlinear memory terms $N_{\gamma,\,q}(u)$, $N_{\gamma,\,p}(u_{t})$, $N_{\gamma,\,p,\,q}(u,\,u_{t})$ on exterior domain, respectively. Blow-up dynamic of solution is deduced by taking advantage of the test function method related to an appropriate harmonic function. It is worth observing that the semilinear viscous Moore-Gibson-Thompson equation with memory terms can be considered as an approximation of viscous Moore-Gibson-Thompson equation with nonlinear terms when $\gamma\rightarrow1^{-}$. Up to author's best knowledge, the results in Theorems 1.1-1.3 are new.- 1 January 2027
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 17 (2) , 1232-1252
BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS
This article is devoted to investigating the initial boundary value problem of semilinear viscous Moore-Gibson-Thompson equation with general initial values and nonlinear memory terms $N_{\gamma,\,q}(u)$, $N_{\gamma,\,p}(u_{t})$, $N_{\gamma,\,p,\,q}(u,\,u_{t})$ on exterior domain, respectively. Blow-up dynamic of solution is deduced by taking advantage of the test function method related to an appropriate harmonic function. It is worth observing that the semilinear viscous Moore-Gibson-Thompson equation with memory terms can be considered as an approximation of viscous Moore-Gibson-Thompson equation with nonlinear terms when $\gamma\rightarrow1^{-}$. Up to author's best knowledge, the results in Theorems 1.1-1.3 are new.- Open Access
- 11 December 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (24) , 3910
The Blow-Up of Solutions to the Cauchy Problem of Semilinear Tricomi Equations with Damping and Mass Terms
This paper is related to the blow-up results of solutions to the Cauchy problem of semilinear generalized Tricomi equations, which contain a scale-invariant damping term and a mass term. The nonlinear term is of the power type in the case of a single equation, and of the power type and combined type in the case of a coupled system. The upper bound estimate for the lifespan of the solution to the problem with a power-type nonlinear term is obtained by applying the test function method. The lifespan estimates of solutions to the coupled system with power nonlinearities and combined nonlinearities are derived using the iteration method. It is worth pointing out that the time-dependent coefficients of the damping term and mass term determine competition between the Strauss critical exponent and Fujita critical exponent.
- 11 December 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (24) , 3910
Open AccessThe Blow-Up of Solutions to the Cauchy Problem of Semilinear Tricomi Equations with Damping and Mass Terms
This paper is related to the blow-up results of solutions to the Cauchy problem of semilinear generalized Tricomi equations, which contain a scale-invariant damping term and a mass term. The nonlinear term is of the power type in the case of a single equation, and of the power type and combined type in the case of a coupled system. The upper bound estimate for the lifespan of the solution to the problem with a power-type nonlinear term is obtained by applying the test function method. The lifespan estimates of solutions to the coupled system with power nonlinearities and combined nonlinearities are derived using the iteration method. It is worth pointing out that the time-dependent coefficients of the damping term and mass term determine competition between the Strauss critical exponent and Fujita critical exponent.
- 1 January 2024
- Published by International Press of Boston in Communications in Mathematical Sciences
- Vol. 22 (2) , 375-393
Lifespan estimates of solutions to the weakly coupled system of semilinear wave equations with space dependent dampings
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2024
- Published by International Press of Boston in Communications in Mathematical Sciences
- Vol. 22 (2) , 375-393
Lifespan estimates of solutions to the weakly coupled system of semilinear wave equations with space dependent dampings
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2023
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 13 (3) , 1190-1208
BLOW-UP OF SOLUTIONS TO THE SEMILINEAR WAVE EQUATIONS WITH FRICTIONAL AND VISCOELASTIC DAMPING TERMS
Our starting point in this paper is to investigate the weakly coupled system of semilinear wave equations with two types of damping terms and combined nonlinearities $|v_{t}|^{p_{1}}+|v|^{q_{1}}$, $|u_{t}|^{p_{2}}+|u|^{q_{2}}$ on exterior domain in $n\,(n\geq1)$ dimensions. Local existence and uniqueness of mild solutions to the problem are established. Moreover, non-existence of global solutions to the problem with power nonlinearities $|u|^{p},\,|v|^{q}$ in the case of coupled system and the problem with power nonlinearity $|u|^{p}$ in the case of single equation are verified. The proofs are based on the test function technique. It is worth noticing that the frictional damping $u_{t}$ is more dominant than the viscoelastic damping $\Delta u_{t}$ when the time trend to infinity. To the best of our knowledge, the blow-up results in Theorems 1.2--1.3 are new.- 1 January 2023
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 13 (3) , 1190-1208
BLOW-UP OF SOLUTIONS TO THE SEMILINEAR WAVE EQUATIONS WITH FRICTIONAL AND VISCOELASTIC DAMPING TERMS
Our starting point in this paper is to investigate the weakly coupled system of semilinear wave equations with two types of damping terms and combined nonlinearities $|v_{t}|^{p_{1}}+|v|^{q_{1}}$, $|u_{t}|^{p_{2}}+|u|^{q_{2}}$ on exterior domain in $n\,(n\geq1)$ dimensions. Local existence and uniqueness of mild solutions to the problem are established. Moreover, non-existence of global solutions to the problem with power nonlinearities $|u|^{p},\,|v|^{q}$ in the case of coupled system and the problem with power nonlinearity $|u|^{p}$ in the case of single equation are verified. The proofs are based on the test function technique. It is worth noticing that the frictional damping $u_{t}$ is more dominant than the viscoelastic damping $\Delta u_{t}$ when the time trend to infinity. To the best of our knowledge, the blow-up results in Theorems 1.2--1.3 are new.- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Control and Related Fields
- Vol. 13 (3) , 946-966
Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term
The main goal of this work is to investigate formation of singularities for solutions to the quasilinear wave equations with damping terms, negative mass terms and divergence form nonlinearities in the critical and sub-critical cases. Upper bound lifespan estimates of solutions are derived by applying the rescaled test function method and iteration technique. The results are the same as corresponding wave equation without damping term and mass term. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems $ 1.1-1.4 $ are new. Moreover, the changing trends of semilinear wave equations are illustrated through numerical simulation.- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Control and Related Fields
- Vol. 13 (3) , 946-966
Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term
The main goal of this work is to investigate formation of singularities for solutions to the quasilinear wave equations with damping terms, negative mass terms and divergence form nonlinearities in the critical and sub-critical cases. Upper bound lifespan estimates of solutions are derived by applying the rescaled test function method and iteration technique. The results are the same as corresponding wave equation without damping term and mass term. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems $ 1.1-1.4 $ are new. Moreover, the changing trends of semilinear wave equations are illustrated through numerical simulation.