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Fujita Equation with Boundary Effect
by Tai-Ping Liu   Shih-Hsien Yu

Vol. 9 No. 2 (2014) P.267~P.282

ABSTRACT

The well-known Fujita analysis for the blow-up and decay of a semilinear heat equation $u_t - \Delta u=u^p$ is studied here for the half-space problem with Robin boundary condition. Our analysis makes use of the explicit construction of Green's functions for the initial-boundary value problem. Our analysis in deriving the adequate expression of the Green's function have provided further development in the explicit construction of the Green's function for a class of partial differential equations.

KEYWORDS
Initial-boundary value problem, Fujita equation, Green’s function, blow up.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary 35K20; Secondary: 35B44, 35A08.

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