Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition

Evolutionary Equation of Inertial Waves in 3-d Multiply Connected Domain with Dirichlet Boundary Condition

We study initial-boundary value problem for an equation of composite type in 3-Dmultiply connected domain. This equation governs nonsteady inertial waves in rotating fluids. The solution of the problem is obtained in the form of dynamic potentials, which density obeys the uniquely solvable integral equation. Thereby the existence theorem is proved. Besides, the uniqueness of the solution is stu...

Boundary Estimates for a Degenerate Parabolic Equation with Partial Dirichlet Boundary Conditions

We study the boundary regularity properties and derive pointwise a priori supremum estimates of weak solutions and their derivatives in terms of suitable weighted L-norms for a class of degenerate parabolic equations that satisfy homogeneous Dirichlet boundary conditions on certain portions of the boundary. Such equations arise in population genetics in the study of models for the evolution of ...

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Homogenization of the Neumann problem for a quasilinear elliptic equation in a perforated domain

Ω(s) = Ω\F (s), where Ω is a domain in R(n ≥ 3), F (s) is a closed set located in the neighbourhood of a (n − 1)-dimensional manifold Γ lying inside Ω. We study the asymptotic behaviour of u(s) as s → ∞, when the set F (s) tends to Γ. Under appropriate conditions, we prove that u(s) converges in suitable topologies to a solution of a limit boundary value problem of transmission type, where the ...

Homogenization of the Stokes equation with mixed boundary condition in a porous medium