Differential and Integral Equations

Boundedness of global solutions of nonlinear diffusion equation with localized reaction term

Pierre Rouchon

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Abstract

We consider some nonlinear heat equations with nonlocal reaction term in space, in smoothly bounded domains. We prove that all global solutions are uniformly bounded, in other words that blow-up in infinite time cannot occur.

Article information

Source
Differential Integral Equations, Volume 16, Number 9 (2003), 1083-1092.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060558

Mathematical Reviews number (MathSciNet)
MR1989542

Zentralblatt MATH identifier
1035.35053

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B35: Stability 35B45: A priori estimates 35K20: Initial-boundary value problems for second-order parabolic equations

Citation

Rouchon, Pierre. Boundedness of global solutions of nonlinear diffusion equation with localized reaction term. Differential Integral Equations 16 (2003), no. 9, 1083--1092. https://projecteuclid.org/euclid.die/1356060558


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