On the Theory of Entropy Sub- And Supersolutions of Nonlinear Degenerate Parabolic Equations.

Autor: Panov, E. Yu.
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Zdroj: Journal of Mathematical Sciences; Oct2024, Vol. 285 Issue 3, p392-416, 25p
Abstrakt: We consider a second-order nonlinear degenerate anisotropic parabolic equation in the case where the flux vector is only continuous and the nonnegative diffusion matrix is bounded and measurable. The concepts of entropy sub- and supersolution of the Cauchy problem are introduced, so that the entropy solution of this problem understood in the sense of Chen–Perthame is both an entropy sub- and supersolution. It is established that the maximum of entropy subsolutions of the Cauchy problem is also an entropy subsolution of this problem. This result is used to prove the existence of the largest entropy subsolution (and the smallest entropy supersolution). It is also shown that the largest entropy subsolution and the smallest entropy supersolution are also entropy solutions. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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