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.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 20 Nov 2020|
|Event||9th International Conference on Lavrentyev Readings on Mathematics, Mechanics and Physics - Novosibirsk, Russian Federation|
Duration: 7 Sep 2020 → 11 Sep 2020