Rekalo A. Qualitative behaviour of solutions of nonlinear parabolic equations in thin two-layer domains

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0404U003416

Thesis Registration Form

0404U003416.pdf

Applicant for

Specialization

  • 01.01.03 - Математична фізика

27-08-2004

Specialized Academic Board

К 64.051.11

V.N. Karazin Kharkiv National University

Essay

The asymptotic dynamics of reaction-diffusion equations in a thin two-layer domain with a junc- tion condition on the interface is given. Global at- tractors and invariant manifolds of the semigroup are objects of the research. Theorems concer- ning continuity of the attractors with respect to Hausdorff metrics and a sufficient condition of stabilization of every trajectory to a single equilibrim point are obtained. It is proved that trajectories converge with an exponential rate to an infinite-dimensional subspace.

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