Global well-posedness of reaction-diffusion equations with non-radial kernel function

Abstract

In this thesis, we study the following reaction-diffusion equation:[Equation] where f is a continuously differentiable function on R , α > 0 is a constant, [sumbol] is a continuous function and is non-radial kernel function. We establish the corresponding comparison principle. Then, we prove the local existence and uniqueness result based on the monotone iteration sequence technique. Finally, certain sufficient conditions on the local nonlinear term that guarantee the existence and uniqueness of global solution are specified.