Analysis Of Blowup For Parabolic Equations With Memory Boundary Condition

There are many nature phenomena could be described by non-local reaction-diffusionequations in the study of biology, chemistry etc. Compared with non-local equation withspatial variant integral, the study of non-local equation with time integral is very insufficient.This paper mainly deals with two parabolic equations with time integral boundary, i.e.memory boundary. We will use the method of super-solution and sub-solution, the integralestimate and the convex method.In Chapter2, we investigate a heat equation with memory boundary condition:Firstly, by constructing appropriate super-solutions and some integral estimate technique, thesufficient conditions for global existence and finite time blow-up are obtained. Secondly,through introducing suitable auxiliary functions and using comparison principle, we provethat in some cases the blow-up can occur only on the boundary of the domain.In Chapter3, we discuss an equation with nonlocal react term and memory boundary:We first obtain the complete classification of global existence and finite time blow-up.Secondly, we study the blow-up set for blow-up solution. We shall prove that under someconditions the blow-up can occur only on the boundary of the domain.