Access the full text.
Sign up today, get DeepDyve free for 14 days.
M. Ben-Artzi, P. Souplet, F. Weissler (2002)
The local theory for viscous Hamilton–Jacobi equations in Lebesgue spacesJournal de Mathématiques Pures et Appliquées, 81
S. Benachour, P. Laurençot (1999)
Global solutions to viscous hamilton-jacob1 equations with irregular initial dataCommunications in Partial Differential Equations, 24
M. Ben-Artzi, H. Koch (1999)
DECAY OF MASS FOR A SEMILINEAR PARABOLIC EQUATIONCommunications in Partial Differential Equations, 24
L. Amour, M. Ben-Artzi (1998)
Global existence and decay for viscous Hamilton-Jacobi equationsNonlinear Analysis-theory Methods & Applications, 31
The large time behaviour of the $ L^q $ -norm of nonnegative solutions to the "anisotropic" viscous Hamilton-Jacobi equation¶¶ $u_t - \Delta u + \sum_{i=1}^m \vert u_{x_i}\vert^{p_i} = 0 \;\;\mbox{ in }\; {\mathbb{R}}_+\times{\mathbb{R}}^N,$ ¶¶is studied for $ q=1 $ and $ q=\infty $ , where $ m\in\{1,\ldots,N\} $ and $ p_i\in [1,+\infty) $ for $ i\in\{1,\ldots,m\} $ . The limit of the $ L^1 $ -norm is identified, and temporal decay estimates for the $ L^\infty $ -norm are obtained, according to the values of the $ p_i $'s. The main tool in our approach is the derivation of $ L^\infty $ -decay estimates for $ \nabla\left(u^\alpha \right), \alpha\in (0,1] $ , by a Bernstein technique inspired by the ones developed by Bénilan for the porous medium equation.
Journal of Evolution Equations – Springer Journals
Published: Feb 1, 2003
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.