BLOW-UP BEHAVIOR FOR A PARABOLIC EQUATION WITH SPATIALLY DEPENDENT COEFFICIENT

摘要

We study the initial boundary value problem and Cauchy problem for the semilinear heat equation with power nonlinearity and spatially dependent coefficient. First, for the initial boundary value problem, we establish several conditions that ensure the origin is not a blow-up point. Then the Cauchy problem for a special case is also studied, Finally, we derive the blow-up rate when the origin is not a blow-up point.