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Very Regular Solutions for the Landau-Lifschitz Equation with Electric Current

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Chinese Annals of Mathematics,Series B 2018年第5期39卷 889-916页

作者： Gilles CARBOU Rida JIZZINI Laboratoire de Mathématiques Appliquées de Pau UMR CNRS 5142 Université de Pau et des Pays de l'Adour Institut de Mathématiques de Bordeaux UMR CNRS 5251 Université de Bordeaux 351 cours de la Libération

The authors consider a model of ferromagnetic material subject to an electric current, and prove the local in time existence of very regular solutions for this model in the scale of H^k spaces. In particular, they des... 详细信息

关键词： Ferromagnetic materials Compatibility conditions existence result

Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1143-1160页

作者： Jing ZHAO Chun Mei GAN Zhen Hai LIU School of Mathematics and Quantitative Economics Guangxi University of Finance and EconomicsNanning 530003P.R.China Guangxi Colleges and Universities Key Laboratory of Optimization Control and Engineering Calculation Guangxi Minzu UniversityNanning 530006P.R.China

The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach ***,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational ***,some topological properties of the solution set are established such as boundedness,closedness and ***,we explore the upper semicontinuity of the solution ***,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).

关键词： Differential parabolic hemivariational inequality Clarke subdifferential hyperbolicparabolic system parabolic-parabolic system existence result

On the Solvability of Degenerate Quasilinear Parabolic Equations of Second Order

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Acta Mathematica Sinica,English Series 2000年第2期16卷 313-324页

作者： Zhenhai Liu Department of Mathematics,Changsha University of Electric Power,Changsha 410077,P.R.China Department of Mathematics Changsha University of Electic Power Changsha 410077 P. R. China

In this paper,we consider nonlinear degenerate quasilinear parabolic initial boundary value problems of second *** results from the theory of pseudomonotone operators,we show that there exists at least one weak soluti... 详细信息

关键词： Quasilinear parabolic Degenerate equation existence result

existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

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Applied Mathematics 2024年第7期15卷 455-463页

作者： Mohamed Karimou Gazibo Duni Yegbonoma Frédéric Zongo Laboratoire de Mathmatiques Fondamentales et Applications (LMFA) Dpartement de Mathmatiques cole Normale Suprieure Universit Abdou Moumouni de Niamey Niamey Niger Laboratoire Interdisciplinaire de Recherche en Sciences Appliques (LIRSA) cole Normale Suprieure Burkina Faso

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

关键词： Lebesgue and Sobolev Spaces with Variable Exponent Weak Solution Entropy Solution Degenerate Parabolic-Hyperbolic Equation Conservation Law Leray Lions Type Operator Neumann Boundary Condition existence result

On Henig Regularization of Material Design Problems for Quasi-Linear p-Biharmonic Equation

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Applied Mathematics 2016年第14期7卷 1547-1570页

作者： Peter Kogut Günter Leugering Ralph Schiel Department of Differential Equations Dnipropetrovsk National University Dnipro Ukraine Department Mathematik Lehrstuhl II Universit&auml t Erlangen-Nürnberg Cauerstr Erlangen Germany

We study a Dirichlet optimal design problem for a quasi-linear monotone p-biharmonic equation with control and state constraints. We take the coefficient of the p-biharmonic operator as a design variable in . In this ... 详细信息

关键词： p-Biharmonic Problem Optimal Design Relaxation Henig Dilating Cone existence result