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Finite-Time Blow-Up and Local Existence for Chemotaxis System with a General memory term

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Journal of Partial Differential Equations 2021年第1期34卷 67-82页

作者： WU Yingdong WU Shaohua CHENG Xin LIU Lei School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

In this paper,we discuss the local existence of weak solutions for a parabolic system modelling chemotaxis with memory term,and we show the finite-time blowup and chemotactic collapse for this *** main methods we used... 详细信息

关键词： parabolic system chemotaxis memory term fixed point theorem blow-up

Existence of Solutions for a Parabolic System Modelling Chemotaxis with memory term

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Journal of Partial Differential Equations 2020年第2期33卷 158-170页

作者： WU Shaohua LIU Lei School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

In this paper,we come up with a parabolic system modelling chemotaxis with memory term,and establish the local existence and uniqueness of weak *** main methods we use are the fixed point theorem and semigroup theory.

关键词： Parabolic system chemotaxis memory term fixed point theorem

Stability in Inverse Problem of Determining Two Parameters for the Moore-Gibson-Thompson Equation with memory terms

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Journal of Systems Science & Complexity 2024年第6期37卷 2368-2389页

作者： FU Songren CHEN Liangbiao ZHANG Ji-Feng Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Automation and Electrical Engineering Zhongyuan University of TechnologyZhengzhou 450007China

In this paper,the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity,which introduce a sort of delay in the dynamics,producing nonlocal effects in *** H¨older stability of simultaneously determining the spatially varying viscosity coefficient and the source term is obtained by means of the key pointwise Carleman estimate for the Moore-Gibson-Thompson *** the sake of generality in mathematical tools,the analysis of this paper is discussed within the framework of Riemannian geometry.

关键词： Carleman estimate memory term Moore-Gibson-Thompson equation stability Riemannian geometry

GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A memory CONDITION AT THE BOUNDARY

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Acta Mathematica Scientia 2014年第3期34卷 729-738页

作者： Jum-Ran KANG Department of Mathematics Dong-A UniversityBusan 604-714Korea

In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

关键词： General decay differential inclusion boundary value problem memory term relaxation function

GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY memory CONDITION

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Acta Mathematica Scientia 2014年第5期34卷 1395-1403页

作者： Sun Hye PARK Center for Education Accreditation Pusan National University

In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.

关键词： transmission problem Kirchhoff type general decay memory term relaxationfunction

EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

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Acta Mathematica Scientia 2013年第2期33卷 505-524页

作者： N. TATAR King Fahd University of Petroleum and Minerals Department of Mathematics & StatisticsDhahran 31261Saudi Arabia

Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions： What if the kernel is tested against a different function （say Gamma） other than the exponential function？ Would there still be stability？ In the affirmative, what kind of decay rate we get？ It is proved that for a non- decreasing function ＂Gamma＂ whose ＂logarithmic derivative＂ is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential.

关键词： Arbitrary decay memory term relaxation function Timoshenko beam vis-coelasticity

EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

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Acta Mathematica Scientia 2012年第6期32卷 2237-2246页

作者： Shun-Tang Wu General Education Center National Taipei University of Technology Taipei 106~ China

The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.

关键词： viscoelastic wave equation kernel exponential decay memory term singular kernel

Dynamics of Plate Equations with memory Driven by Multiplicative Noise on Bounded Domains

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1492-1521页

作者： Mohamed Y. A. Bakhet Abdelmajid Ali Dafallah Jing Wang Qiaozhen Ma Fadlallah Mustafa Mosa Ahmed Eshag Mohamed Paride O. Lolika Makur Mukuac Chinor School of Mathematics University of Juba Juba South Sudan Department of Mathematics Faculty of Petroleum and Hydrology Engineering Alsalam University Almugled Sudan College of Mathematics and Statistics Northwest Normal University Lanzhou China Department of Mathematics and Physics Faculty of Education University of Kassala Kassala Sudan Department of Mathematics School of Education University of Juba Juba South Sudan

This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.

关键词： Plate Equations Random Attractors memory term Dynamical Systems

Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact

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Open Journal of Modelling and Simulation 2021年第4期9卷 391-406页

作者： Yahyeh Souleiman Mikaël Barboteu Mathematics and Computer Science Laboratory Campus Balbala University of Djibouti Balbala Djibouti Mathematics and Physics Laboratory University of Perpignan Perpignan France

This paper represents a continuation of [1] and [2]. Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

关键词： Viscoelastic Material Sliding Frictional Contact Normal Compliance Unilateral Constraint memory term Variational Approximation Finite Element Error Estimate Numerical Simulations