To the theory of entropy sub-solutions of degenerate nonlinear parabolic equations |
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| Authors: | Evgeny Yu Panov |
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| Institution: | Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, Russian Federeation and Peoples' Friendship University of Russia (RUDN University), Moscow, Russian Federation |
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| Abstract: | We prove existence of the largest entropy sub-solution and the smallest entropy super-solution to the Cauchy problem for a nonlinear degenerate parabolic equation with only continuous flux and diffusion functions. Applying this result, we establish the uniqueness of entropy solution with periodic initial data. The more general comparison principle is also proved in the case when at least one of the initial functions is periodic. |
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| Keywords: | Cauchy problem comparison principle conservation laws entropy sub- and super-solutions nonlinear parabolic equations |
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