scholarly journals A Class of One-Dimensional Degenerate Parabolic Equations.

1985 ◽  
Author(s):  
John A. Nohel
Keyword(s):  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
One Dimensional ◽  
Degenerate Parabolic

Complete quenching phenomenon and instantaneous shrinking of support of solutions of degenerate parabolic equations with nonlinear singular absorption

2019 ◽  
Vol 149 (5) ◽  
pp. 1323-1346 ◽  
Author(s):  
Nguyen Anh Dao ◽  
Jesus Ildefonso Díaz ◽  
Huynh Van Kha
Keyword(s):  
Parabolic Equations ◽  
Dirichlet Boundary ◽  
Degenerate Parabolic Equations ◽  
One Dimensional ◽  
Finite Speed Of Propagation ◽  
Nonnegative Solutions ◽  
Degenerate Parabolic ◽  
Speed Of Propagation ◽  
The One ◽  
Quenching Phenomenon

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.

Sign in / Sign up

Export Citation Format

Share Document