Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

Global Existence and Asymptotic Behavior of Weak Solutions to Nonlinear Thermoviscoelastic Systems with Clamped Boundary Conditions

This paper is concerned with global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions. The constitutive assumptions for the Helmholtz free energy include the model for the study of phase transitions in shape memory alloys. To describe phase transitions between different configurat...

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

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...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Asymptotic Free Energy of a System with Periodic Boundary Conditions

A v-dimensional classical particle system in a torus, i.e., in a rectangular box with periodic boundary conditions, is considered in a canonical ensemble. Subject to mild restrictions over and above the usual stability and tempering conditions it is proved that the thermodynamic limit for the torus exists and is identical with that for systems contained in normal domains with boundaries or wall...