Differential and Integral Equations

Blow-up behavior for semilinear heat equations with boundary conditions

Kazuhiro Ishige and Noriko Mizoguchi

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We study the blow-up behavior of solutions of the semilinear heat equations under the Dirichlet boundary condition or the Neumann boundary condition. We prove the nondegeneracy of blow-up of the solutions. Furthermore, we give a result on the blow-up rate of the solutions under the Neumann boundary condition.

Article information

Differential Integral Equations, Volume 16, Number 6 (2003), 663-690.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35K20: Initial-boundary value problems for second-order parabolic equations


Ishige, Kazuhiro; Mizoguchi, Noriko. Blow-up behavior for semilinear heat equations with boundary conditions. Differential Integral Equations 16 (2003), no. 6, 663--690. https://projecteuclid.org/euclid.die/1356060606

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