Global and blowup solutions of semilinear heat equation involving the square root of the Laplacian

摘要

In this paper, we consider nonlinear parabolic equations involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition. We use the method on harmonic extension to study the existence and asymptotic estimates of global solutions, as well as the blowup of the parabolic equation.