Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations

Abstract

Abstract We consider second-order linear parabolic partial differential inequalities that include nonlocal zeroth-order quantities. For these, we establish minimum principles that highlight the interplay between the regularity of their coefficients, the growth/decay rate of their solutions and the integrability of the nonlocal interaction terms. Subsequently we utilize these minimum principles to establish comparison principles for related semilinear integrodifferential inequalities. We illustrate these principles via their relation to nonlocal reaction–diffusion equations.

Keywords

• Minimum principles
• Comparison Principles
• Nonlinear nonlocal integrodifferential operator
• Integrodifferential inequality