On qualitative properties of solutions of quasilinear mixed problems for equations of parabolic type

In this paper mixed problems for quasilinear equations of parabolic type are studied. Criteria are established for the negativeness of the spectrum of the linearized problems in the neighborhood of steady state solutions, and necessary and sufficient conditions are obtained for the stability of the steady state solutions of the nonlinear problems. The domains of attraction are also investigated. The results are illustrated by a series of examples.
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