FINITE VELOCITY AND SPACE LOCALIZATION IN NON- DIVERGENT CROSS-DIFFUSION SYSTEMS WITH VARIABLE DENSITY
DOI:
https://doi.org/10.52754/16948645_2023_1_24Keywords:
Задача Коши, кросс-диффузия, переменной плотность, конечной скорость, поглощение, локальное существование, глобальное решение, blow-up свойствоAbstract
The Cauchy problem for a cross-diffusion parabolic system of non-divergent equations with variable density and time-dependent absorption is investigated.
In this paper, by constructing a solution of the Zeldovich-Barenblatt type for the system, nonlinear effects of finite velocity and space localization of heat conductivity are established. The regularization method and the upper-lower solution technique are used to show the local existence of a solution for a nonlinear degenerate parabolic system. The existence of a global solution is discussed, the blow-up property of the solution is established. The local existence and uniqueness of the classical solution is proved.
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