Abstract
It is sbown that solutions of an equation for a nonlinear parabolic system contained in a region R of (x,t,u,w) space, satisfy comparison theorems of the second order in one dependent variable. These lead to uniqueness proofs for the Dirichlet and related problems. The comparison theoroms are used in conjunction with theorems on a priori estimatcs for and existence of solutions of linear parabolic equations of the second order due to Friedman to derive corresponding solutions of the nonlinear parabolic system. The methods used are readily generalized and applied to systems involving many dependent variables such as those describing the multigroup diffusion of neutrons in fissionable matter or the flux of heat and moisture through porous solids. (L.N.N.)
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