Khomchenko L. Asymptotical solutions to the Dirichlet and Neumann boundary value problems for singularly perturbed parabolic type partial differential equations with impulses.

The thesis is devoted to solving the problem on constructing asymptotical solutions to Dirichlet and Neumann boundary value problems for singularly perturbed parabolic equations with variable coefficients and impulses at fixed moments of time. The algorithm of constructing asymptotical solutions of the problems mentioned above is developed on the base of Vishyk-Lusternik approach. The ground of the algorithm is given and corresponding theorems on estimation of difference between exact and approximated solutions is proved. To construct asymptotical solutions in exact form we formulate corresponding Cauchy problems and boundary value problems for boundary and angular functions, later we prove solvability of these problems and obtain lemmas on properties of boundary and angular functions from which the asymptotical solutions consist of. The results of the thesis can be applied within the research of different phenomenon and processes of physics, chemistry, biology, medicine, economics, etc, that can be characterized by quick change of some characteristics and mathematical description of which is given by singularly perturbed nonlinear parabolic differential equations with variable coefficients and contain impulsive effects conditions at fixed moments.