Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions

Abstract

We investigate a class of semilinear parabolic and elliptic problems withfractional dynamic boundary conditions. We introduce two new operators, theso-called fractional Wentzell Laplacian and the fractional Steklov operator,which become essential in our study of these nonlinear problems. Besidesgiving a complete characterization of well-posedness and regularity ofbounded solutions, we also establish the existence of finite-dimensionalglobal attractors and also derive basic conditions for blow-up.