Topological structure of solution sets to parabolic problems

Abstract

In this paper we deal with the Peano phenomenon for general initial-boundary value problems of quasilinear parabolic equations with arbitrary even order space derivatives.

The nonlinearity is assumed to be a continuous or continuously Fréchet differentiable function. Using a method of transformation to an operator equation and employing the theory of proper, Fredholm (linear and nonlinear) and Nemitskiĭ operators, we study the existence of solution of the given problem and qualitative and quantitative structure of its solution and bifurcation sets. These results can be applied to the different technical and natural science models.