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Small amplitude homogenization applied to models of non-periodic fibrous materials

David Manceau (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process. To this end, the two homogenized models are simplified using the small amplitude homogenization procedure of Tartar, both in conduction and in elasticity. A new small amplitude homogenization expansion formula for a mixture of anisotropic elastic materials is also derived and allows us to obtain a third simplified model.

Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

Makoto Nakamura, Tohru Ozawa (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space ℝ n with order s < n / 2 . The assumptions on the nonlinearities are described in terms of power behavior p 1 at zero and p 2 at infinity such as 1 + 4 / n ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLS and NLKG, and 1 + 4 / ( n - 1 ) ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLW.

Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem

Milan Štědrý, Otto Vejvoda (1983)

Aplikace matematiky

This paper deals with a system of equations describing the motion of viscous electrically conducting incompressible fluid in a bounded three dimensional domain whose boundary is perfectly conducting. The displacement current appearing in Maxwell’s equations, ϵ E t is not neglected. It is proved that for a small periodic force and small positive there exists a locally unique periodic solution of the investigated system. For ϵ → 0 , these solutions are shown to convergeto a solution of the simplified (and...

Small time-periodic solutions to a nonlinear equation of a vibrating string

Eduard Feireisl (1987)

Aplikace matematiky

In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.

Smooth bifurcation for a Signorini problem on a rectangle

Jan Eisner, Milan Kučera, Lutz Recke (2012)

Mathematica Bohemica

We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. We describe smooth branches of smooth nontrivial solutions bifurcating from the trivial solution branch in eigenvalues of the linearized problem. In particular, the contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tools of the proof...

Smooth regularity for solutions of the Levi Monge-Ampère equation

Francesca Lascialfari, Annamaria Montanari (2001)

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

We present a smooth regularity result for strictly Levi convex solutions to the Levi Monge-Ampère equation. It is a fully nonlinear PDE which is degenerate elliptic. Hence elliptic techniques fail in this situation and we build a new theory in order to treat this new topic. Our technique is inspired to those introduced in [3] and [8] for the study of degenerate elliptic quasilinear PDE’s related to the Levi mean curvature equation. When the right hand side has the meaning of total curvature of a...

Smooth solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...

Currently displaying 341 – 360 of 1682