Regularity Results for a Nonlinear Elliptic-Parabolic System with Oscillating Coefficients

DOI10.4208/ATA.OA-2020-0021zbMath1499.35444arXiv1911.05863MaRDI QIDQ5864744

Xiangsheng Xu

Publication date: 8 June 2022

Published in: Analysis in Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.05863

zbMATH Keywords

quadratic nonlinearityoscillating coefficientsthermistor problem

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Initial-boundary value problems for mixed-type systems of PDEs (35M33)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solutions of fourth-order parabolic equation modeling thin film growth
• Degenerate parabolic equations
• Exponential integrability of temperature in the thermistor problem.
• Blow-up of solutions of nonlinear heat equations
• Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor
• A heat balance integral model of the thermistor
• A variety of finite difference methods to the thermistor with a new modified electrical conductivity.
• On the existence of bounded temperature in the thermistor problem with degeneracy
• Existence and long time behaviour of solutions to obstacle thermistor equations
• Local and global existence of solutions to a fourth-order parabolic equation modeling kinetic roughening and coarsening in thin films
• A local partial regularity theorem for weak solutions of degenerate elliptic equations and its application to the thermistor problem.
• Local partial regularity theorems for suitable weak solutions of a class of degenerate systems
• Optimal control of a thermistor problem with vanishing conductivity
• Global existence of strong solutions to a biological network formulation model in 2+1 dimensions
• Nonlinear diffusion in the Keller-Segel model of parabolic-parabolic type
• Stationary solutions to the thermistor problem
• Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions
• W 2,p -Solvability of the Dirichlet Problem for Nondivergence Elliptic Equations with VMO Coefficients
• The Thermistor Problem: Existence, Smoothness Uniqueness, Blowup
• Partial regularity of solutions to a class of degenerate systems
• Regularity of solutions of the thermistor problem
• Logarithmic upper bounds for weak solutions to a class of parabolic equations

This page was built for publication: Regularity Results for a Nonlinear Elliptic-Parabolic System with Oscillating Coefficients