Initial-boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermodiffusion in solid body
type: Item
instance of: scholarly article
title: Initial-boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermodiffusion in solid body
zbMATH Open document ID: 0969.35075
DOI: 10.4171/ZAA/942
author: Yanyan Li
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2001-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/48901
review text: Summary: We prove a theorem about existence, uniqueness and regularity of the solution to an initial-boundary value problem for the nonlinear coupled parabolic system \[ c(\theta_1,\theta_2) \partial_t\theta_1- a^1_{\alpha\beta}(\theta_1, \theta_2,\nabla\theta_1, \nabla\theta_2) {\partial^2\theta_1\over\partial x_\alpha\partial x_\beta}+ d(\theta_1, \theta_2,\nabla\theta_1, \nabla\theta_2){\partial\theta_2\over \partial t}= Q_1, \] \[ n(\theta_1,\theta_2) \partial_t\theta_2- a^2_{\alpha,\beta}(\theta_1, \theta_2,\nabla\theta_1, \nabla\theta_2) {\partial^2\theta_2\over \partial x_\alpha\partial x_\beta}+ d(\theta_1,\theta_2, \nabla\theta_1, \nabla\theta_2) {\partial\theta_1\over\partial t}= Q_2. \] Such a system appears in the thermodiffusion in solid bodies. In our proof we use an energy method, methods of Sobolev spaces, semigroup theory and the Banach fixed point theorem.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1453208
zbMATH Keywords: homogeneous Dirichlet boundary conditions
zbMATH Keywords: energy method
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: semigroup theory
zbMATH Keywords: Banach fixed point theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1453208