ON THE METHOD OF STATIONARY STATES FOR QUASI-LINEAR PARABOLIC EQUATIONS

A method is presented for investigating the space-time structure of unbounded nonnegative solutions of quasilinear parabolic equations of the form , whereis a nonlinear elliptic operator. Three examples are considered in detail: the Cauchy problem for the equation where and are constants; the boundary value problem in and the Cauchy problem for the system It is assumed that at the point the solution grows without bound as The derivation of an estimate of the solution near , is based on an analysis of an appropriate family of stationary solutions a parameter. It is shown that the behavior of a solution as depends to large extent on the structure of the envelope In particular, if then grows without bound as at points arbitrarily far from for determines a lower bound for in a neighborhood of T0, X=0. © 1990 American Mathematical Society.