Existence and long time behaviour of solutions to obstacle thermistor equations

Walter Allegretto, Yanping Lin, Shuqing Ma

Research output: Journal article publicationJournal articleAcademic researchpeer-review

25 Citations (Scopus)

Abstract

In this paper we introduce an obstacle thermistor system. The existence of weak solutions to the steady-state systems and capacity solutions to the time dependent systems are obtained by a penalized method under reasonable assumptions for the initial and boundary data. At the same time, we prove that there exists a uniform absorbing set for nonnegative initial data in L2(Ω). Finally for smooth initial data a global attractor to the system is obtained by a series of Campanato space arguments.
Original languageEnglish
Pages (from-to)757-780
Number of pages24
JournalDiscrete and Continuous Dynamical Systems
Volume8
Issue number3
Publication statusPublished - 1 Jan 2002
Externally publishedYes

Keywords

  • Capacity solutions
  • Global attractors
  • Obstacle thermistor equations

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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