Por Ivan Kuznetsov (Lavrentyev Institute of Hydrodynamics – Siberian Division of the Russian Academy of Sciences, Novosibirsk State University).

Abstract: Extending the results obtained in [1] we have proved the existence and the uniqueness of entropy solutions to ultra-parabolic equations with initial, boundary and, correspondingly, impulsive conditions. The case without impulsive conditions has been treated in [2,3].The main challenge of the Cauchy-Dirichlet problem being under our study is that boundary conditions are formulated as inequalities.
(Joint work with Sergey Sazhenkov)

References:

[1] M. Escobedo, J.L. Vázquez, and E. Zuazua, Entropy solutions for diffusion-convection equations with partial diffusivity, Trans. Amer. Math. Soc. Vol. 343 (1994), 829-842.
[2] I.V. Kuznetsov, Genuinely nonlinear forward-backward ultra-parabolic equations, Sib. Electronic Math. Rep., Vol. 14 (2017), 710-731.
[3] I.V. Kuznetsov, and S.A. Sazhenkov, Quasi-solutions of genuinely nonlinear forwardbackward ultra-parabolic equations, Journal of Physics: Conference Series, Vol. 894 (2017), 012046.