On Certain 3-Dimensional Limit Boundary Value Problems
Vladimir Vasilyev
Abstract
The paper is devoted to studying limit behavior for a solution of model elliptic pseudo-differential equation with some integral boundary condition in 4-wedge conical canonical 3D singular domain with two parameters. It is shown that the solution of such boundary value problem can have a limit with respect to endpoint values of the parameters in appropriate Sobolev–Slobodetskii space if the boundary function is a solution of a special functional singular integral equation.
Topics & Concepts
MathematicsMathematical analysisBoundary value problemSobolev spaceSingular solutionLimit (mathematics)Mixed boundary conditionFree boundary problemSingular boundary methodConical surfaceSingular functionWedge (geometry)Domain (mathematical analysis)Singular integralIntegral equationGeometryBoundary element methodFinite element methodPhysicsThermodynamicsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in Engineering