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Relaxation and numerical approximation of a two-fluid two-pressure diphasic model

Annalisa Ambroso, Christophe Chalons, Frédéric Coquel, Thomas Galié (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural...

Remark on the null-condition for the nonlinear wave equation

Nickolay Tzvetkov (2000)

Bollettino dell'Unione Matematica Italiana

Dimostriamo l'esistenza della soluzione globale per un sistema di equazioni delle onde con nonlinearità quadratica dipendente dalle variabili spazio-tempo. Come in [3] la tecnica è basata sulla trasformazione di Penrose.

Remarks on Carleman estimates and exact controllability of the Lamé system

Oleg Yu. Imanuvilov, Masahiro Yamamoto (2002)

Journées équations aux dérivées partielles

In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

Remarks on the qualitative behavior of the undamped Klein-Gordon equation

Esquivel-Avila, Jorge A. (2017)

Proceedings of Equadiff 14

We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature.

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