The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary

The boundary-value problem in domains with very rapidly oscillating boundary

The asymptotic behavior of solutions to the boundary-value probb lems posed in domains with very rapidly oscillating locally periodic boundary, is studied. For various kinds of boundary conditions the limiting problems are found and the estimates of the residual are given. Also, we construct an additional term of the asymptotics to improve the estimates of the residual. Le probllme de condition...

Second-Order Boundary Value Problem with Integral Boundary Conditions

NON-POLYNOMIAL QUARTIC SPLINE SOLUTION OF BOUNDARY-VALUE PROBLEM

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

THE STEFAN PROBLEM WITH KINETIC FUNCTIONS AT THE FREE BOUNDARY

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed