Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

Abstract

This paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results.

Keywords

• functional partial differential equation
• nonlocal condition
• strong solution
• analytic compact semigroup
• fractional power operator
• α-norm
• 34g20
• 34k30
• 35d35