Abstract
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.
Highlights
This paper is concerned with the study of global and blowup solutions of semilinear heat equation involving a nonlocal positive operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions
We obtain a contradiction, which completes the proof of Theorem
Summary
This paper is concerned with the study of global and blowup solutions of semilinear heat equation involving a nonlocal positive operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. ), the corresponding energy functional I : H / ( ) → R is defined as follows: In [ ], Tan first introduced the energy method to study the existence and asymptotic estimates of global solution of
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