A nonlocal p-Laplacian evolution equation with Neumann boundary conditions |
| |
Authors: | F. Andreu, J.M. Maz n, J.D. Rossi,J. Toledo |
| |
Affiliation: | aDepartament de Matemàtica Aplicada, Universitat de València, Valencia, Spain;bDepartament d'Anàlisi Matemàtica, Universitat de València, Valencia, Spain;cIMDEA Matematicas, C-IX, Universitat Autonoma, Campus Cantoblanco, Madrid, Spain;dDepartamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina |
| |
Abstract: | In this paper we study the nonlocal p-Laplacian type diffusion equation, If p>1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut=div(|u|p−2u) with homogeneous Neumann boundary conditions. We prove existence and uniqueness of a strong solution, and if the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in L∞(0,T;Lp(Ω)) to the solution of the p-Laplacian with homogeneous Neumann boundary conditions. The extreme case p=1, that is, the nonlocal analogous to the total variation flow, is also analyzed. Finally, we study the asymptotic behavior of the solutions as t goes to infinity, showing the convergence to the mean value of the initial condition. |
| |
Keywords: | Nonlocal diffusion p-Laplacian Total variation flow Neumann boundary conditions |
本文献已被 ScienceDirect 等数据库收录! |
|