Mathematics – Analysis of PDEs
Scientific paper
2012-01-17
Mathematics
Analysis of PDEs
20 pages 1 figure
Scientific paper
This paper is concerned with weak solutions of the degenerate viscous Hamilton-Jacobi equation $$\partial_t u-\Delta_p u=|\nabla u|^q,$$ with Dirichlet boundary conditions in a bounded domain $\Omega\subset\mathbb{R}^N$, where $p>2$ and $q>p-1$. With the goal of studying the gradient blow-up phenomenon for this problem, we first establish local well-posedness with blow-up alternative in $W^{1, \infty}$ norm. We then obtain a precise gradient estimate involving the distance to the boundary. It shows in particular that the gradient blow-up can take place only on the boundary. A regularizing effect for $u_t$ is also obtained.
No associations
LandOfFree
Well-posedness and gradient blow-up estimate near the boundary for a Hamilton-Jacobi equation with degenerate diffusion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Well-posedness and gradient blow-up estimate near the boundary for a Hamilton-Jacobi equation with degenerate diffusion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-posedness and gradient blow-up estimate near the boundary for a Hamilton-Jacobi equation with degenerate diffusion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-97923