Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774609 | Journal of Mathematical Analysis and Applications | 2017 | 26 Pages |
Abstract
We deal with a nonlocal nonlinear evolution problem of the formâ¬RnÃRJ(xây,tâs)|vâ¾(y,s)âv(x,t)|pâ2(vâ¾(y,s)âv(x,t))dyds=0 for (x,t)âRnÃ[0,â). Here pâ¥2, J:Rn+1âR is a nonnegative kernel, compactly supported inside the set {(x,t)âRn+1:tâ¥0} with â¬RnÃRJ(x,t)dxdt=1 and vâ¾ stands for an extension of a given initial value f, that is,vâ¾(x,t)={v(x,t)tâ¥0,f(x,t)t<0. For this problem we prove existence and uniqueness of a solution. In addition, we show that the solutions approximate viscosity solutions to the local nonlinear PDE ââuâpâ2ut=Îpu when the kernel is rescaled in a suitable way.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gaston Beltritti, Julio D. Rossi,