Author:
Dao Nguyen Anh,Díaz Jesus Ildefonso,Kha Huynh Van
Abstract
AbstractThis paper deals with nonnegative solutions of the one-dimensional degenerate parabolic equations with zero homogeneous Dirichlet boundary condition. To obtain an existence result, we prove a sharp estimate for |ux|. Besides, we investigate the qualitative behaviours of nonnegative solutions such as the quenching phenomenon, and the finite speed of propagation. Our results of the Dirichlet problem are also extended to the associated Cauchy problem on the whole domain ℝ. In addition, we also consider the instantaneous shrinking of compact support of nonnegative solutions.
Publisher
Cambridge University Press (CUP)
Reference33 articles.
1. Abstract results on the finite extinction time property: application to a singular parabolic equation;Belaud;J. Convex. Anal.,2010
2. A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena
3. Nonuniqueness in the quenching problem
4. The fast diffusion equation with strong absorption: the instantaneous shrinking phenomenon;Borelli;Rend. Istit. Mat. Univ. Trieste,1994
5. Pointwise gradient estimates of solutions of one dimensional nonlinear parabolic problems;Benilan;J. Evol. Equ.,2004
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献