Open AccessEntropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term
Author(s) -
И. В. Кузнецов,
Sergey Sazhenkov
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1666/1/012025
Subject(s) - mathematics , dirac delta function , mathematical analysis , boundary value problem , limiting , entropy (arrow of time) , cauchy problem , term (time) , parabolic partial differential equation , minor (academic) , nonlinear system , dirichlet boundary condition , partial differential equation , initial value problem , physics , quantum mechanics , mechanical engineering , political science , law , engineering
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.