Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501604 | Journal of Differential Equations | 2005 | 36 Pages |
Abstract
We prove the existence and the uniqueness of strong solutions for the viscous Hamilton-Jacobi equation: ut-Îu=a|âu|p,t>0,xâΩ with Neumann boundary condition, and initial data μ0, a continuous function. The domain Ω is a bounded and convex open set with smooth boundary, aâR,aâ 0 and p>0. Then, we study the large time behavior of the solution and we show that for pâ(0,1), the extinction in finite time of the gradient of the solution occurs, while for p⩾1 the solution converges uniformly to a constant, as tââ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Saı¨d Benachour, Simona Dabuleanu,