Sen Ming
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Sen Ming has a total of 30 co-authors. Here are the top co-authors by number of shared publications:
Xiongmei Fan
Data Science and Technology, North University of China, Taiyuan 030051, China
9 shared publicationsYeqin Su
Department of Securities and Futures, Southwestern University of Finance and Economics, Chengdu, China
9 shared publicationsShaoyong Lai
Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, People's Republic of China
7 shared publicationsJiayi Du
Department of Mathematics, North University of China, Taiyuan 030051, China
6 shared publications- Xiongmei Fan
Data Science and Technology, North University of China, Taiyuan 030051, China
5 shared publications Wei Han
Department of Mathematics, North University of China, Taiyuan 030051, China
3 shared publications
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
Blow-Up of Nonlinear Wave Equations with Memory Terms in High-Dimensional Schwarzschild Spacetime
This paper is concerned with the blow-up of solutions to the Cauchy problems of nonlinear wave equations with memory terms in high-dimensional Schwarzschild spacetime. The blow-up results and upper-bound estimates of the lifespans of the solutions to initial-value problems of nonlinear wave equations are obtained by using the appropriate test function method related to the Riemann–Liouville fractional derivative. For the wave equation with combined nonlinear memory terms, we improve the upper-bound estimate of the lifespan of the solution in the existing literature. The lifespan estimates of the solutions are obtained without assuming that the support of the initial values should be far away from a black hole. It is worth mentioning that the crucial difficulty is the setting of the test function framework for the different types of nonlinear memory terms. To the best of our knowledge, the results in Theorems 1–3 are new.
Open AccessBlow-Up of Nonlinear Wave Equations with Memory Terms in High-Dimensional Schwarzschild Spacetime
This paper is concerned with the blow-up of solutions to the Cauchy problems of nonlinear wave equations with memory terms in high-dimensional Schwarzschild spacetime. The blow-up results and upper-bound estimates of the lifespans of the solutions to initial-value problems of nonlinear wave equations are obtained by using the appropriate test function method related to the Riemann–Liouville fractional derivative. For the wave equation with combined nonlinear memory terms, we improve the upper-bound estimate of the lifespan of the solution in the existing literature. The lifespan estimates of the solutions are obtained without assuming that the support of the initial values should be far away from a black hole. It is worth mentioning that the crucial difficulty is the setting of the test function framework for the different types of nonlinear memory terms. To the best of our knowledge, the results in Theorems 1–3 are new.
- Open Access
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Electronic Research Archive
- Vol. 34 (4) , 2483-2510
Blow-up for coupled systems of semilinear damped wave equations on the Heisenberg group
The main purpose of this paper is to study behaviors of solutions to the Cauchy problem for coupled systems of semilinear damped wave equations with power nonlinearities on the Heisenberg group, where the Fujita critical exponent is determined. By means of the Bihari inequality as well as the Gagliardo-Nirenberg-type inequality and the contraction mapping principle, the local well-posedness of the Cauchy problem is successfully proved. Combining energy estimates and decay estimates together with a contradiction argument, the global existence of solutions is also demonstrated. At the same time, the blow-up results and upper bound estimation of the solutions is derived by using the test function technique. Our main new contribution is the derivation of a fundamental inequality utilized in weighted energy estimates, as well as the selection of exponents in the scaling of two convex functions for constructing test functions.
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Electronic Research Archive
- Vol. 34 (4) , 2483-2510
Open AccessBlow-up for coupled systems of semilinear damped wave equations on the Heisenberg group
The main purpose of this paper is to study behaviors of solutions to the Cauchy problem for coupled systems of semilinear damped wave equations with power nonlinearities on the Heisenberg group, where the Fujita critical exponent is determined. By means of the Bihari inequality as well as the Gagliardo-Nirenberg-type inequality and the contraction mapping principle, the local well-posedness of the Cauchy problem is successfully proved. Combining energy estimates and decay estimates together with a contradiction argument, the global existence of solutions is also demonstrated. At the same time, the blow-up results and upper bound estimation of the solutions is derived by using the test function technique. Our main new contribution is the derivation of a fundamental inequality utilized in weighted energy estimates, as well as the selection of exponents in the scaling of two convex functions for constructing test functions.
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 27, 90-114
Global rough solutions to the coupled nonlinear Schrödinger equations
The global well-posedness of the Cauchy problem for coupled system of fourth-order nonlinear Schrödinger equations is studied. The almost conservation law for modified energy of coupled systems is proved in low regularity space $ H^s(\mathbb{R}^4)\,(\frac{1}{2}<s<2) $ by establishing the conservation laws of mass and energy as well as applying the $ I $ method. Based on the scale invariance, the relation between initial energy and scaling energy is derived. In addition, the polynomial growth estimate of modified energy is obtained. Therefore, global well-posedness for the Cauchy problem of coupled system in $ H^s(\mathbb{R}^4)\,(\frac{8}{7}< s<2) $ is obtained. It is shown that the spatial norms of solutions grow polynomially with respect to the time variable. It is worth pointing out that the solutions of the coupled system exist uniquely and their norms depend continuously on the $ H^s(\mathbb{R}^4) $ norms of initial values.- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 27, 90-114
Global rough solutions to the coupled nonlinear Schrödinger equations
The global well-posedness of the Cauchy problem for coupled system of fourth-order nonlinear Schrödinger equations is studied. The almost conservation law for modified energy of coupled systems is proved in low regularity space $ H^s(\mathbb{R}^4)\,(\frac{1}{2}<s<2) $ by establishing the conservation laws of mass and energy as well as applying the $ I $ method. Based on the scale invariance, the relation between initial energy and scaling energy is derived. In addition, the polynomial growth estimate of modified energy is obtained. Therefore, global well-posedness for the Cauchy problem of coupled system in $ H^s(\mathbb{R}^4)\,(\frac{8}{7}< s<2) $ is obtained. It is shown that the spatial norms of solutions grow polynomially with respect to the time variable. It is worth pointing out that the solutions of the coupled system exist uniquely and their norms depend continuously on the $ H^s(\mathbb{R}^4) $ norms of initial values.- Open Access
Existence of Blow-Up Solution to the Cauchy Problem of Inhomogeneous Damped Wave Equation
This paper is concerned with the non-existence of a global solution to the initial value problem of the inhomogeneous damped wave equation with a nonlinear memory term and a nonlinear gradient term. The critical exponent and formation of singularity of solution are closely related to symmetry in the study of blow-up dynamics for nonlinear wave equations, which provides a profound mathematical tool for analyzing the explosion of solutions within finite time. The proofs of blow-up results of solutions are based on the test function method, where the test function is variable separated. The influences of two types of damping terms, two types of nonlinearities, and an inhomogeneous term on exponents of the problem in blow-up cases are explained. It is worth pointing out that the inhomogeneous term in the problem is discussed with respect to the exponent in three cases (namely, , , and ). As far as we know, the results in Theorems 1–4 are new.Open AccessExistence of Blow-Up Solution to the Cauchy Problem of Inhomogeneous Damped Wave Equation
This paper is concerned with the non-existence of a global solution to the initial value problem of the inhomogeneous damped wave equation with a nonlinear memory term and a nonlinear gradient term. The critical exponent and formation of singularity of solution are closely related to symmetry in the study of blow-up dynamics for nonlinear wave equations, which provides a profound mathematical tool for analyzing the explosion of solutions within finite time. The proofs of blow-up results of solutions are based on the test function method, where the test function is variable separated. The influences of two types of damping terms, two types of nonlinearities, and an inhomogeneous term on exponents of the problem in blow-up cases are explained. It is worth pointing out that the inhomogeneous term in the problem is discussed with respect to the exponent in three cases (namely, , , and ). As far as we know, the results in Theorems 1–4 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.
- 17 June 2024
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 540 (2)
Blow-up of solutions to the wave equations with memory terms in Schwarzschild spacetime
- 17 June 2024
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 540 (2)
Blow-up of solutions to the wave equations with memory terms in Schwarzschild spacetime
- Open Access
- 1 January 2024
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 9 (10) , 26854-26876
Blow-up of solutions for coupled wave equations with damping terms and derivative nonlinearities
This work was concerned with the weakly coupled system of semi-linear wave equations with time dependent speeds of propagation, damping terms, and derivative nonlinear terms in generalized Einstein-de Sitter space-time on $ \mathbb{R}^n $. Under certain assumptions about the indexes $ k_1, \, k_2 $, coefficients $ \mu_1, \, \mu_2 $, and nonlinearity exponents $ p, \, q $, applying the iteration technique, finite time blow-up of local solutions to the small initial value problem of the coupled system was investigated. Blow-up region and upper bound lifespan estimate of solutions to the problem were established. Compared with blow-up results in the previous literature, the new ingredient relied on that the blow-up region of solutions obtained in this work varies due to the influence of coefficients $ k_1, \, k_2 $.- 1 January 2024
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 9 (10) , 26854-26876
Open AccessBlow-up of solutions for coupled wave equations with damping terms and derivative nonlinearities
This work was concerned with the weakly coupled system of semi-linear wave equations with time dependent speeds of propagation, damping terms, and derivative nonlinear terms in generalized Einstein-de Sitter space-time on $ \mathbb{R}^n $. Under certain assumptions about the indexes $ k_1, \, k_2 $, coefficients $ \mu_1, \, \mu_2 $, and nonlinearity exponents $ p, \, q $, applying the iteration technique, finite time blow-up of local solutions to the small initial value problem of the coupled system was investigated. Blow-up region and upper bound lifespan estimate of solutions to the problem were established. Compared with blow-up results in the previous literature, the new ingredient relied on that the blow-up region of solutions obtained in this work varies due to the influence of coefficients $ k_1, \, k_2 $. - 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
- Open Access
- 4 April 2023
- Published by Springer Nature in Boundary Value Problems
- Vol. 2023 (1) , 1-25
Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain
- 4 April 2023
- Published by Springer Nature in Boundary Value Problems
- Vol. 2023 (1) , 1-25
Open AccessBlow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain