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学者姓名：王术
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Abstract ：
In this paper, we construct a family of global-in-time solutions of the 3-D full compressible Navier-Stokes (N-S) equations with temperature-dependent transport coefficients (including viscosity and heat-conductivity), and show that at arbitrary times and arbitrary strength this family of solutions converges to planar rarefaction waves connected to the vacuum as the viscosity vanishes in the sense of L infinity(R3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>\infty ({\mathbb {R}}<^>3)$$\end{document}. We consider the Cauchy problem in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}<^>3$$\end{document} with perturbations of the infinite global norm, particularly, periodic perturbations. To deal with the infinite oscillation, we construct a suitable ansatz carrying this periodic oscillation such that the difference between the solution and the ansatz belongs to some Sobolev space and thus the energy method is feasible. The novelty of this paper is that the viscosity and heat-conductivity are temperature-dependent and degeneracies caused by vacuum. Thus the a priori assumptions and two Gagliardo-Nirenberg type inequalities are essentially used. Next, more careful energy estimates are carried out in this paper, by studying the zero and non-zero modes of the solutions, we obtain not only the convergence rate concerning the viscosity and heat conductivity coefficients but also the exponential time decay rate for the non-zero mode.
Keyword ：
35Q31 35Q31 35Q30 35Q30 76N06 76N06 35Q35 35Q35 76N10 76N10
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| GB/T 7714 | Hou, Meichen , Liu, Lingjun , Wang, Shu et al. Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients [J]. | MATHEMATISCHE ANNALEN , 2024 . |
| MLA | Hou, Meichen et al. "Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients" . | MATHEMATISCHE ANNALEN (2024) . |
| APA | Hou, Meichen , Liu, Lingjun , Wang, Shu , Xu, Lingda . Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients . | MATHEMATISCHE ANNALEN , 2024 . |
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Abstract ：
In this paper, we study the asymptotic behavior of the non-autonomous stochastic 3D Brinkman-Forchheimer equations on unbounded domains. We first define a continuous non-autonomous cocycle for the stochastic equations, and then prove that the existence of tempered random attractors by Ball's idea of energy equations. Furthermore, we obtain that the tempered random attractors are periodic when the deterministic non-autonomous external term is periodic in time.
Keyword ：
non-autonomous non-autonomous random attractors random attractors unbounded domains unbounded domains Stochastic Brinkman-Forchheimer equations Stochastic Brinkman-Forchheimer equations
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| GB/T 7714 | Wang, Shu , Si, Mengmeng , Yang, Rong . RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC BRINKMAN-FORCHHEIMER EQUATIONS ON UNBOUNDED DOMAINS [J]. | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS , 2022 , 21 (5) : 1621-1636 . |
| MLA | Wang, Shu et al. "RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC BRINKMAN-FORCHHEIMER EQUATIONS ON UNBOUNDED DOMAINS" . | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 21 . 5 (2022) : 1621-1636 . |
| APA | Wang, Shu , Si, Mengmeng , Yang, Rong . RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC BRINKMAN-FORCHHEIMER EQUATIONS ON UNBOUNDED DOMAINS . | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS , 2022 , 21 (5) , 1621-1636 . |
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Abstract ：
The quasineutral limit and the mixed layer problem of the bipolar drift-diffusion model for semiconductors with different mobilities are studied in one dimensional space in this paper. For the general smooth doping profile, the general initial data and the different mobilities of electrons and holes, the quasineutral limit is proven by the matched asymptotic expansion method of singular perturbation problem and the energy method.
Keyword ：
quasineutral limit quasineutral limit mobility mobility Drift-diffusion model Drift-diffusion model mixed layer mixed layer
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| GB/T 7714 | Liu, Chundi , Wang, Shu . Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities [J]. | RESULTS IN MATHEMATICS , 2022 , 77 (5) . |
| MLA | Liu, Chundi et al. "Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities" . | RESULTS IN MATHEMATICS 77 . 5 (2022) . |
| APA | Liu, Chundi , Wang, Shu . Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities . | RESULTS IN MATHEMATICS , 2022 , 77 (5) . |
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Abstract ：
An impulsive integrated pest management system with diffusion is investigated within this paper. The conditions for pest eradication of the impulsive system without natural enemies are established based on the Krein-Rutman theorem and the comparison principle for parabolic equations. Integrated pest management can be achieved at an exponential rate, when the principal eigenvalues of the auxiliary system is large enough. Numerical simulations are presented to demonstrate the theoretical results. A discussion is given at the end.
Keyword ：
Integrated pest management Integrated pest management pest control pest control eigenvalue problem eigenvalue problem diffusion diffusion
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| GB/T 7714 | Hongling, Zhou , Lin, Shen , Shu, Wang . Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity [J]. | JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS , 2022 , 35 (1) : 31-48 . |
| MLA | Hongling, Zhou et al. "Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity" . | JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS 35 . 1 (2022) : 31-48 . |
| APA | Hongling, Zhou , Lin, Shen , Shu, Wang . Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity . | JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS , 2022 , 35 (1) , 31-48 . |
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Abstract ：
In this paper, we are concerned with the global existence of generalized solutions of one-dimensional time-dependent Thomas-Fermi equations of quantum theory of atoms. We will use the vanishing artificial viscosity method. First, a special flux approximate is introduced to ensure the uniform boundedness of the electric field E-epsilon,E-sigma and the a priori L-infinity estimate, 0 < 2 sigma <= n(epsilon,sigma) <= M(t), (sic)(u(epsilon,sigma)(sic) <= M(t), where M(t) could tend to infinity as the time t tends to infinity, on the viscosity-flux approximate solutions (n(epsilon,sigma), u(epsilon,sigma)). Second, a technique, to apply the maximum principle to the combination of the Riemann invariants and (sic)(-infinity)(x) n(epsilon,sigma) (y, t)- 2 sigma dy, deduces the uniform L-infinity estimate, 0 < 2 sigma <= n(epsilon,sigma) < M, (sic)u(epsilon,sigma & nbsp;)(sic) <= M, independent of the time t and epsilon, sigma. Finally, the compensated compactness theory is applied to prove the almost everywhere convergence of (n(epsilon,sigma), u(epsilon,sigma)) as epsilon and (sigma) tend to zero. The limit (n(x, t), u(x, t)) is a global generalized solution. (c) 2022 Elsevier Ltd. All rights reserved.
Keyword ：
Viscosity method Viscosity method Maximum principle Maximum principle equations equations Global generalized solution Global generalized solution Compensated compactness method Compensated compactness method Time-dependent Thomas-Fermi Time-dependent Thomas-Fermi
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| GB/T 7714 | Wang, Shu , Ren, Yabo . The global existence of generalized solutions to the time-dependent Thomas-Fermi equations [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2022 , 219 . |
| MLA | Wang, Shu et al. "The global existence of generalized solutions to the time-dependent Thomas-Fermi equations" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 219 (2022) . |
| APA | Wang, Shu , Ren, Yabo . The global existence of generalized solutions to the time-dependent Thomas-Fermi equations . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2022 , 219 . |
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Abstract ：
In this article, we consider the blowup phenomenon of smooth solutions to the isentropic compressible quantum hydrodynamic model (QHD) with the initial density of compact support in arbitrary space dimensions.
Keyword ：
compressible quantum hydrodynamic model compressible quantum hydrodynamic model smooth solutions smooth solutions blowup blowup
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| GB/T 7714 | Zhang, Jie , Wang, Shu , Geng, Fan . Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2022 , 45 (17) : 10917-10924 . |
| MLA | Zhang, Jie et al. "Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 45 . 17 (2022) : 10917-10924 . |
| APA | Zhang, Jie , Wang, Shu , Geng, Fan . Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2022 , 45 (17) , 10917-10924 . |
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Abstract ：
In this paper, we are concerned with the existence of weak solutions of the time-dependent Thomas-Fermi equations. We derive approximate solutions by the fractional step Lax-Friedrichs scheme and establish uniform boundedness of approximate solutions. Based on the uniform energy-type estimates, we establish that the entropy dissipation measures of the weak solution of the one-dimensional time-dependent Thomas-Fermi equations for weak entropy-entropy flux pairs, generated by compactly supported C0 & INFIN; test functions, are confined in a compact set in Hloc-1. We prove that the Young measure must be a Dirac measure by the Tartar-Murat commutator relation. The convergence of approximate solutions is established by using the compensated compactness method.
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| GB/T 7714 | Wang, Shu , Ren, Yabo . Weak solutions to the Cauchy problem of the time-dependent Thomas-Fermi equations [J]. | JOURNAL OF MATHEMATICAL PHYSICS , 2022 , 63 (6) . |
| MLA | Wang, Shu et al. "Weak solutions to the Cauchy problem of the time-dependent Thomas-Fermi equations" . | JOURNAL OF MATHEMATICAL PHYSICS 63 . 6 (2022) . |
| APA | Wang, Shu , Ren, Yabo . Weak solutions to the Cauchy problem of the time-dependent Thomas-Fermi equations . | JOURNAL OF MATHEMATICAL PHYSICS , 2022 , 63 (6) . |
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Abstract ：
In this note we study the global wellposedness of a two-dimensional incompressible Navier-Stokes fluid structure interaction(FSI) model. The existence and unique-ness of the global strong and smooth solution to the initial boundary value problem for one class of the FSI model in the two-dimensional case, which is one model of two-dimensional incompressible Navier-Stokes equations coupled by the two-dimensional wave equation by the suitable boundary conditions at the interface boundary, are obtained for any smooth initial data under the assumption of the suitable compatibility conditions on the initial data at the interface boundary and external boundary of the domain. '(c) 2022 Elsevier Ltd. All rights reserved.
Keyword ：
interaction model interaction model w t = u w t = u Existence and uniqueness Existence and uniqueness Global strong and smooth solutions Global strong and smooth solutions Incompressible fluid-structure Incompressible fluid-structure
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| GB/T 7714 | Shen, Lin , Wang, Shu . Note on the global wellposedness of two-dimensional incompressible Navier-Stokes fluid structure interaction model [J]. | APPLIED MATHEMATICS LETTERS , 2022 , 140 . |
| MLA | Shen, Lin et al. "Note on the global wellposedness of two-dimensional incompressible Navier-Stokes fluid structure interaction model" . | APPLIED MATHEMATICS LETTERS 140 (2022) . |
| APA | Shen, Lin , Wang, Shu . Note on the global wellposedness of two-dimensional incompressible Navier-Stokes fluid structure interaction model . | APPLIED MATHEMATICS LETTERS , 2022 , 140 . |
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Abstract ：
We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative two-phase flow system described by two-dimentional compressible Euler and Navier-Stokes equations through drag force. In this paper, we show the planar rarefaction wave to a non-conservative compressible two-phase model is asymptotically stable under small initial perturbation in H-3. The main difficulties overcome in this paper come from the non-viscosity of one fluid and the interaction between two fluids caused by drag force. The stability result is proved by the energy method.
Keyword ：
planar rarefaction wave planar rarefaction wave asymptotic stability asymptotic stability energy method energy method Two-phase flow Two-phase flow
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| GB/T 7714 | Wang, Shu , Zhao, Yixuan . ASYMPTOTIC STABILITY OF PLANAR RAREFACTION WAVE TO A MULTI-DIMENSIONAL TWO-PHASE FLOW [J]. | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B , 2022 , 28 (1) : 623-647 . |
| MLA | Wang, Shu et al. "ASYMPTOTIC STABILITY OF PLANAR RAREFACTION WAVE TO A MULTI-DIMENSIONAL TWO-PHASE FLOW" . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 28 . 1 (2022) : 623-647 . |
| APA | Wang, Shu , Zhao, Yixuan . ASYMPTOTIC STABILITY OF PLANAR RAREFACTION WAVE TO A MULTI-DIMENSIONAL TWO-PHASE FLOW . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B , 2022 , 28 (1) , 623-647 . |
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Abstract ：
Global in time weak solutions to the alpha-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to alpha-model regularization for the three dimension compressible Euler-Poisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies gamma > 4/3.
Keyword ：
alpha-model regularization for Euler-Poisson equations alpha-model regularization for Euler-Poisson equations Faedo-Galerkin method Faedo-Galerkin method Global weak solutions Global weak solutions
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| GB/T 7714 | Ren, Yabo , Guo, Boling , Wang, Shu . GLOBAL WEAK SOLUTIONS TO THE alpha-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS [J]. | ACTA MATHEMATICA SCIENTIA , 2021 , 41 (3) : 679-702 . |
| MLA | Ren, Yabo et al. "GLOBAL WEAK SOLUTIONS TO THE alpha-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS" . | ACTA MATHEMATICA SCIENTIA 41 . 3 (2021) : 679-702 . |
| APA | Ren, Yabo , Guo, Boling , Wang, Shu . GLOBAL WEAK SOLUTIONS TO THE alpha-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS . | ACTA MATHEMATICA SCIENTIA , 2021 , 41 (3) , 679-702 . |
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