The Cauchy problem for a system of quasilinear parabolic equations of chemical kinetics type

The Cauchy problem for the class of quasilinear parabolic systems of reaction—diffusion type is considered. Under appropriate assumptions regarding the nonlinearities and the initial functions, the nonlocal solvability of this problem and the stabilization of its solution, uniform with respect to the space variables, are established.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 242–261, 1992.