Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term

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Abstract

The Cauchy-Dirichlet problem for the genuinely nonlinear ultra-parabolic equation with the piece-wise smooth minor term is considered. The minor term depends on a small positive parameter and collapses to the one-sided Dirac delta function as this parameter tends to zero. As the result, we arrive at the limiting initial-boundary value problem for the impulsive ultra-parabolic equation. The peculiarity is that the standard entropy solution of the problem for the impulsive equation generally is not unique. In this report, we propose a rule for selecting the 'proper' entropy solution, relying on the limiting procedure in the original problem incorporating the smooth minor term.

Original languageEnglish
Article number012025
JournalJournal of Physics: Conference Series
Volume1666
Issue number1
DOIs
Publication statusPublished - 20 Nov 2020
Event9th International Conference on Lavrentyev Readings on Mathematics, Mechanics and Physics - Novosibirsk, Russian Federation
Duration: 7 Sep 202011 Sep 2020

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