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

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

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

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Veröffentlicht in:Communications in Mathematics 2020-07, Vol.28 (1), p.67-88
Hauptverfasser: Sabri, Abdelali, Jamea, Ahmed, Alaoui, Hamad Talibi
Format: Artikel
Sprache:eng
Schlagworte:
35A02
35J60
35J65
35J92
Degenerate parabolic problem
entropy solution
existence
Mathematics
Rothe’s method
semi-discretization
weighted Sobolev space
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Zusammenfassung:In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic (·)-Laplacian problem with Dirichlet-type boundary conditions and data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.
ISSN:1804-1388
2336-1298
DOI:10.2478/cm-2020-0006