The initial boundary value problems for the semilinear diffusion equations with data in L^p spaces

Abstract

In this paper, I have established conditions under which the existence and uniqueness of weak solutions of some Semilinear diffusion equations with initial and boundary data in fractional LL ^p spaces can be established in a bounded domain with smooth boundary The interest of this method relies on the fact that it is by successive approximations and hence amenable to numerical treatment. The paper also considers the semigroups theory on the existence of weak classical solutions.

Keywords:

• Banach
• bilinear
• classical
• contraction
• diffusion
• fixed-point
• operator
• semigroup
• semilinear
• trilinear
• weak

AMS:

• 35K15
• 35K55
• 45G05