Boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian resolved with respect to the derivative

Abstract

We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Levy Laplacian ∆ L resolved with respect to the derivative $$ \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right),{\Delta_L}U\left( {t,x} \right)} \right) $$ in fundamental domains of a Hilbert space.