Existence and long time behaviour of solutions to obstacle thermistor equations

Walter Allegretto; Yanping Lin; Shuqing Ma

Existence and long time behaviour of solutions to obstacle thermistor equations

Walter Allegretto, Yanping Lin, Shuqing Ma

Research output: Journal article publication › Journal article › Academic research › peer-review

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 language	English
Pages (from-to)	757-780
Number of pages	24
Journal	Discrete and Continuous Dynamical Systems
Volume	8
Issue number	3
Publication status	Published - 1 Jan 2002
Externally published	Yes

Keywords

Capacity solutions
Global attractors
Obstacle thermistor equations

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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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.",

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AU - Lin, Yanping

AU - Ma, Shuqing

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N2 - 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.

AB - 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.

KW - Capacity solutions

KW - Global attractors

KW - Obstacle thermistor equations

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M3 - Journal article

VL - 8

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 3

ER -

Existence and long time behaviour of solutions to obstacle thermistor equations

Abstract

Keywords

ASJC Scopus subject areas

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Cite this