Topological structure of solution sets to parabolic problems

Vladimír Ďurikovič, Monika Ďurikovičová

DOI: http://dx.doi.org/10.12775/TMNA.2005.016

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 Nemitski\u\i\ 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.

Keywords


35K35; 35K60; 35B22; 35B32;35B38; 47A53; 47H09; 47H10; 47H30; 58B15; 58D25

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