Free boundary problem for a system of parabolic equations of the reaction-diffusion type

This paper considers a free boundary problem for a system of quasi-linear parabolic equations in one dimension. Nonlinear problems with a free boundary are studied using a method based on constructing a priori estimates. For the solutions of the problem, apriory estimates of Shauder type are established. On the base of apriory estimates, the existence and uniqueness theorems are proved.

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