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Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys

Pierluigi Colli (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.

Mathematical study of rotational incompressible non-viscous flows through multiply connected domains

Miloslav Feistauer (1981)

Aplikace matematiky

The paper is devoted to the study of the boundary value problem for an elliptic quasilinear second-order partial differential equation in a multiply connected, bounded plane domain under the assumption that the Dirichlet boundary value conditions on the separate components of the boundary are given up to additive constants. These constants together with the solution of the equation considered are to be determined so as to fulfil the so called trainling conditions. The results have immediate applications...

Mathematics of Invisibility

Allan Greenleaf, Yaroslav Kurylev, Matti Lassas, Gunther Uhlmann (2007)

Journées Équations aux dérivées partielles

We will describe recent some of the recent theoretical progress on making objects invisible to electromagnetic waves based on singular transformations.

Matrix triangulation of hypoelliptic boundary value problems

R. A. Artino, J. Barros-Neto (1992)

Annales de l'institut Fourier

Given a hypoelliptic boundary value problem on ω × [ 0 , T ) with ω an open set in R n , ( n > 1 ) , we show by matrix triangulation how to reduce it to two uncoupled first order systems, and how to estimate the eigenvalues of the corresponding matrices. Parametrices for the first order systems are constructed. We then characterize hypoellipticity up to the boundary in terms of the Calderon operator corresponding to the boundary value problem.

Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher, Besma Ben Ali (2007)

Annales de l’institut Fourier

We show various L p estimates for Schrödinger operators - Δ + V on ℝ n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of - Δ + V and their gradients.

Maximal regularity and viscous incompressible flows with free interface

Senjo Shimizu (2008)

Banach Center Publications

We consider a free interface problem for the Navier-Stokes equations. We obtain local in time unique existence of solutions to this problem for any initial data and external forces, and global in time unique existence of solutions for sufficiently small initial data. Thanks to global in time L p - L q maximal regularity of the linearized problem, we can prove a global in time existence and uniqueness theorem by the contraction mapping principle.

Currently displaying 81 – 100 of 515