Nguyen Manh Hung
On the smoothness of the generalized solution of a parabolic system in domains with conic points on the boundary
Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 857–864
We consider the first initial boundary-value problems for parabolic systems in domains with conic points on a boundary. We study the smoothness of their solutions with respect to spatial variables.
On the Smoothness of a Generalized Solution of the First Initial Boundary-Value Problem for Strongly Parabolic Systems in a Cylinder with Nonsmooth Base with Respect to Time Variable
Ukr. Mat. Zh. - 2004. - 56, № 1. - pp. 78-87
We consider the first initial boundary-value problem for strongly parabolic systems in an infinite cylinder with nonsmooth boundary. We establish conditions for the existence of generalized solutions, an estimate for this solutions, and an estimate for the derivative of the solution.
On the Asymptotic Behavior of Solutions of the First Initial Boundary-Value Problems for Parabolic Equations
Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1143-1152
We consider the first initial boundary-value problem for a strongly parabolic system on an infinite cylinder with nonsmooth boundary. We prove some results on the existence, uniqueness, and asymptotic behavior of solutions as t → ∞.
On the Stability of Semilinear Nonautonomous Evolution Equations in Banach Spaces and Its Application to Strongly Parabolic Equations
Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1714-1719
The paper is concerned with the exponential stability of the zero solution of strongly nonautonomous parabolic equations. Conditions are found on time-dependent coefficients of a parabolic equation under which its solutions converge exponentially to 0 as t → ∞.