We consider dynamical and quasi-static thermoelastic contact problems in R modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-sta...

We propose a model for the folding of rock under the compression of tectonic plates. This models an elastic rock layer imbedded in a viscous foundation by a fourth-order parabolic equation with a nonlinear constraint. The large-time behaviour of solutions of this problem is examined and found to be of approximately self-similar form.

A series of lectures on topics of current research interest in applied mathematics under the direction of the Conference Board of the Mathematical Sciences, supported by the National Science Foundation and published by SIAM. Temam, Roger. Navier-stokes equations and nonlinear functional analysis / Roger Temam. — 2nd ed.

We study a mathematical problem describing the frictionless adhesive contact between an elastic body and a foundation. The adhesion process is modelled by a surface variable, the bonding field, and the contact is modelled with a normal compliance condition; the tangential shear due to the bonding field is included; the elastic constitutive law is assumed to be nonlinear and the process is quasi...

The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini’s conditions and adhesion. The evolution of bonding field is described by a nonlin...

A complete 3-D Canonical Piecewise-Linear (CPWL) representation is developed constructively in this paper. The key to the representation is the establishment of the explicit functional formulation of basis function. It is proved that basis function is the most elementary generating function from which a fully general 3-D PWL function can be formulated. This CPWL representation laid a solid theo...

During the last two decades the program of ‘proof mining’ emerged which uses tools from mathematical logic (so-called proof interpretations) to systematically extract explicit quantitative information (e.g. rates of convergence) from prima facie nonconstructive proofs (e.g. convergence proofs). This has been applied particularly successful in the context of nonlinear analysis: fixed point theor...