Buhrii O. M.
On the Existence of Mild Solutions of the Initial-Boundary-Value Problems for the Petrovskii-Type Semilinear Parabolic Systems with Variable Exponents of Nonlinearity
Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 435–444
We study the initial-boundary-value problem with general homogeneous boundary conditions for the Petrovskii-type semilinear parabolic systems with variable exponents of nonlinearity in a cylindrical domain. The existence of mild solutions of this problem is proved.
Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 612-628
We investigate a mixed problem for a class of parabolic-type equations with double nonlinearity and minor terms that do not degenerate and whose indexes of nonlinearity are functions of spatial variables. These problems are considered in the generalized Lebesgue and Sobolev spaces. We obtain conditions for the existence of the generalized solution of this problem by using the Galerkin method.
Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 867-878
We obtain conditions for the existence and uniqueness of a solution of a parabolic variational inequality that is a generalization of the equation of polytropic elastic filtration without initial conditions. The class of uniqueness of a solution of this problem consists of functions that increase not faster than e −μt , μ > 0, as t → −∞.