Entropy Solutions for Nonlinear Degenerate Problems

1999 ◽  
Vol 147 (4) ◽  
pp. 269-361 ◽  
Author(s):  
José Carrillo
Keyword(s):  
Entropy Solutions ◽  
Degenerate Problems ◽  
Nonlinear Degenerate

scholarly journals Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and L1-data

2020 ◽  
Vol 28 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Abdelali Sabri ◽  
Ahmed Jamea ◽  
Hamad Talibi Alaoui
Keyword(s):  
Variable Exponent ◽  
Main Tool ◽  
Entropy Solutions ◽  
Parabolic Problems ◽  
L1 Data ◽  
Variable Exponent Sobolev Spaces ◽  
Degenerate Parabolic ◽  
Type Boundary ◽  
Degenerate Parabolic Problems ◽  
Nonlinear Degenerate

AbstractIn the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic p(·)-Laplacian problem with Dirichlet-type boundary conditions and L1 data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.

scholarly journals Perturbed nonlinear degenerate problems in RN

2009 ◽  
Vol 36 (2) ◽  
pp. 213-223
Author(s):  
A. El Khalil ◽  
S. El Manouni ◽  
M. Ouanan
Keyword(s):  
Degenerate Problems ◽  
Nonlinear Degenerate

scholarly journals On the Theory of Entropy Solutions of Nonlinear Degenerate Parabolic Equations

2020 ◽  
Vol 66 (2) ◽  
pp. 292-313
Author(s):  
E. Yu. Panov
Keyword(s):  
Cauchy Problem ◽  
Entropy Solution ◽  
Quasilinear Equation ◽  
Entropy Solutions ◽  
Degenerate Parabolic Equations ◽  
The Cauchy Problem ◽  
Periodic Initial Data ◽  
Degenerate Parabolic ◽  
Diffusion Function ◽  
Nonlinear Degenerate

We consider a second-order nonlinear degenerate parabolic equation in the case when the flux vector and the nonstrictly increasing diffusion function are merely continuous. In the case of zero diffusion, this equation degenerates into a first order quasilinear equation (conservation law). It is known that in the general case under consideration an entropy solution (in the sense of Kruzhkov-Carrillo) of the Cauchy problem can be non-unique. Therefore, it is important to study special entropy solutions of the Cauchy problem and to find additional conditions on the input data of the problem that are sufficient for uniqueness. In this paper, we obtain some new results in this direction. Namely, the existence of the largest and the smallest entropy solutions of the Cauchy problem is proved. With the help of this result, the uniqueness of the entropy solution with periodic initial data is established. More generally, the comparison principle is proved for entropy suband super-solutions, in the case when at least one of the initial functions is periodic. The obtained results are generalization of the results known for conservation laws to the parabolic case.

scholarly journals Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal

2021 ◽  
Vol 6 (4) ◽  
pp. 3974-3995
Author(s):  
Abdelgader Siddig ◽  
◽  
Zhichang Guo ◽  
Zhenyu Zhou ◽  
Boying Wu ◽  
...  
Keyword(s):  
Fourth Order ◽  
Noise Removal ◽  
Entropy Solutions ◽  
Degenerate Problem ◽  
Nonlinear Degenerate
Sign in / Sign up

Export Citation Format

Share Document