期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 532, 期 1, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127926
关键词
Non-local diffusion; Non-local Neumann boundary value; Semi-linear equation
This paper studies the non-local diffusion problem with non-local Neumann boundary condition. Integration by parts formulas similar to the Laplacian are established, and the existence, uniqueness, and maximum principle of the solution are proved. The properties of the Neumann condition for one equation and for a family of equations are also investigated.
In this paper, we study the non-local diffusion problem J * u - u - ut = f (u) with non-local Neumann boundary condition. We first establish some integration by parts formulas similar to the Laplacian. Then the existence and uniqueness of the solution and the maximum principle are proved. We also investigate the properties of the Neumann condition for one equation and for a family of equations. (c) 2023 Elsevier Inc. All rights reserved.
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