On a phase transition model in ferromagnetism

This paper deals with the limiting behavior of a phase transition model in ferromagnetism. The model describes the three-dimensional evolution of both thermodynamic and electromagnetic properties of the ferromagnetic material. We are concerned with the passage from 3D to 2D in the theory of the paramagnetic-ferromagnetic transition. We identify the limit problem by using the so-called energy method.     

A dynamic contact problem in thermoviscoelasticity with two temperatures

This work is concerned with the study of a one-dimensional dynamic contact problem arising in thermoviscoelasticity with two temperatures. The existence and uniqueness of a solution to the continuous problem is established using the Faedo–Galerkin method. A finite element approximation is proposed, a convergence result given and some numerical simulations described.     

An a priori error analysis of a type III thermoelastic problem with two porosities

In this work, we study, from the numerical point of view, a type III thermoelastic model with double porosity. The thermomechanical problem is written as a linear system composed of hyperbolic partial differential equations for the displacements and the two porosities, and a parabolic partial differential equation for the thermal displacement. An existence and uniqueness result is recalled. Then, we perform its a priori error numerical analysis approximating the resulting variational problem by using the finite element method and the implicit Euler scheme. The linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are shown to demonstrate the accuracy of the approximations and the dependence of the solution on a coupling coefficient.     

Analyticity of thermoelastic plates with dynamical boundary conditions

We consider a thermoelastic plate with dynamical boundary conditions.Using the contradictionargument of Pazy’s well-known analyticity criterion and P.D.E.estimates, we prove that the corresponding C_0semigroup is analytic,hence exponentially stable.     

A mixed finite element method for the unilateral contact problem in elasticity

In this paper, we provide a new mixed finite element approximation of the varia-tional inequality resulting from the unilateral contact problem in elasticity. We use the continuous piecewise P2-P1 finite element to approximate the displacement field and the normal stress component on the contact region. Optimal convergence rates are obtained under the reasonable regularity hypotheses. Numerical example verifies our results.     

An inverse contact problem in the theory of elasticity

In this paper, we discuss an inverse problem in elasticity for determining a contact domain and stress on this domain. We show that this problem is an ill‐posed problem, and we establish the uniqueness and L²‐conditional stability estimation for the stress. Copyright © 1999 John Wiley & Sons, Ltd.     

An inverse problem for the quasistatic thermoelastic system on the unit Disk

An inverse problem for a quasistatic, linearized, thermoelastic system on the unit disk is formulated as a minimization problem, by use of function theoretic methods and a potential representation.     

Layer dynamics and phase transition for non-linear thermoviscoelasticity

In this article, we study the dynamics of transition layers for a system of 1D non-linear thermoviscoelasticity with non-monotone stress–strain relation.     

The Yamabe problem on quaternionic contact manifolds

By constructing normal coordinates on a quaternionic contact manifold M, we can osculate the quaternionic contact structure at each point by the standard quaternionic contact structure on the quaternionic Heisenberg group. By using this property, we can do harmonic analysis on general quaternionic contact manifolds, and solve the quaternionic contact Yamabe problem on M if its Yamabe invariant satisfies λ(M) < λ(ℍ ⁿ ). Mathematics Subject Classification (2000) 53C17, 53D10, 35J70     

Existence of a solution for a Signorini contact problem for Maxwell-Norton materials

The aim of this article is to study the quasistatic evolutionof a Maxwell–Norton three-dimensional viscoelastic solidwith contact constraints. After introducing the appropiate functionalframework, we will discretize the problem in time using an implicitscheme whose resultant variational inequality is well posed.By using monotonicity arguments together with compensated compactnesstechniques, we will prove that the corresponding discrete solutionconverges to a solution of the continuous problem.     

The weak survival/strong survival phase transition for the contact process on a homogeneous tree

The contact process on a homogeneous tree of degree 3 or larger is known to have two survival phases: weak and strong. In the weak survival phase, the "Malthusian parameter" (the Hausdorff dimension of the set of ends of the tree in which the infection survives) is less than half the Hausdorff dimension of the entire boundary. It is shown that if the expected infection time of a vertex is bounded by a constant times the probability of infection, then the critical exponent for the Malthusian parameter is at least 1/2. Received: 30 June 2002     

Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations

We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two‐phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ? ‐periodic, fixed reference domain, we establish the well‐posedness of the model and derive a number of ? ‐independent a priori estimates. Via a two‐scale convergence argument, we then show that the ? ‐dependent solutions converge to solutions of a corresponding upscaled model with distributed time‐dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.     

The Riemann problem for thermoelastic materials with phase change

We consider the Riemann problem for a system of conservation laws related to a phase transition problem. The system is nonisentropic and we treat the case where the latent heat is not zero. We study the cases where the initial data are given in the same phase and in the different phases. The role of the entropy condition is studied as well as the kinetic relation and the entropy rate admissibility criterion. We confine our attention to the case where the speeds of phase boundaries are close to zero. This is one interesting case in physics. We discuss the number of phase boundaries consistent with the above criteria and the uniqueness and nonuniqueness issue of the solution to the Riemann problem.     

Numerical study of phase transition in thermoviscoelasticity

We study the spatially periodic problem of thermoviscoelasticity with non-monotone structure relations. By pseudo-spectral method, we demonstrate numerically phase transitions for certain symmetric initial data. Without symmetry, the simulations show that a translation occurs for the phase boundary.     

A contact problem in generalized thermoelasticity

In this work we study a one-dimensional contact problem in generalized thermoelasticity under the Green-Lindsay theory. Unilateral contact with an elastic obstacle is assumed. We consider the quasi-static and the fully dynamic situations. We prove existence and uniqueness results and propose finite element approximations in space with backward Euler discretization in time. Stability results are given and some numerical experiments reported. The second sound effect of heat conduction is observed in the simulations.     

Numerical analysis of a contact problem between two thermoviscoelastic beams

We propose and analyze in this article a finite element approximation, based on a penalty formulation, to a quasi‐static unilateral contact problem between two thermoviscoelastic beams. An error bound is given and some numerical experiments discussed. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 644–661, 2011     

High-energy solutions for a phase transition problem

In this article we study the existence and profile of high-energy solutions for the phase transition model

     

A nonlinear transmission problem for a compound plate with thermoelastic part

In this paper, we study a nonlinear transmission problem for a plate that consists of thermoelastic and isothermal parts. The problem generates a dynamical system in a suitable Hilbert space. The main result is the proof of the asymptotic smoothness of this dynamical system. We also prove the existence of a compact global attractor in special cases when the nonlinearity is of Berger type or scalar. Copyright © 2012 John Wiley & Sons, Ltd.     

A two phase elliptic singular perturbation problem with a forcing term

We study the following two phase elliptic singular perturbation problem:

Δu^ε=β_ε(u^ε)+f^ε,