Asymptotic behavior of solutions to the Stefan problem with a kinetic condition at the free boundary

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

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

Asymptotic behavior of solutions to wave equations with a memory condition at the boundary ∗

In this paper, we study the stability of solutions for wave equations whose boundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially...

Pergamon Asymptotic Behavior of Energy Solutions to a Two-dimensional Semilinear Problem with Mixed Boundary Condition

where: • f~ is a C °'1 and bounded domain in Rz; • 0f~ consists of two pieces F0 and F1, where the one-dimensional Hausdorff measure of F o is greater than 0; • F0 is smooth and F1 is piecewise smooth; • F0 and 1"1 are relatively closed in 0f~; • v is the unit outer normal of f~; • p is a large parameter. In this work, we shall only consider the least energy solutions, although the method can b...

Asymptotic Behavior of Energy Solutions to a Two Dimensional Semilinear Problem with Mixed Boundary Condition