FUJITA EQUATION WITH BOUNDARY EFFECT

The well-known Fujita analysis for the blow-up and decay of a semilinear heat equa- tion utu = u p is studied here for the half-space problem with Robin boundary con- dition. 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.