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Free Boundary Problems: Theory and Applications

Isabel Narra Figueiredo ; José Francisco Rodrigues ; Lisa Santos (eds.)

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Analysis; Numerical Analysis; Partial Differential Equations

Disponibilidad
Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-3-7643-7718-2

ISBN electrónico

978-3-7643-7719-9

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Birkhäuser Basel 2007

Cobertura temática

Tabla de contenidos

High-order Techniques for Calculating Surface Tension Forces

M. Sussman; M. Ohta

In this paper we develop further the “height fraction” technique for computing curvature directly from volume fractions. In particular we, (1) develop a systematic approach for calculating curvature from volume fractions which is accurate to any order, and (2) we test the second-order “height fraction” technique on the following two-phase problems: (1) the break-up of a cylindrical column of liquid due to Rayleigh-capillary instability, (2) surface tension induced droplet oscillations and (3) the steady motion of gas bubbles rising in liquid.

Pp. 425-434

Simulation of a Model of Tumors with Virus-therapy

Youshan Tao; Qian Guo

We consider a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate inside them, and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. However, a major factor influencing the efficacy of virus agents is the immune response that may limit the replication and spread of the replication-competent virus. The immune response is cytokine-mediated. The expression of viruses in tumor cells sensitize cells to lysis by the TNF (tumor necrosis factor) cytokine. The competition between tumor cells, a replication-competent virus and an immune response is modelled as a free boundary problem for a nonlinear system of partial differential equations, where the free boundary is the surface of the tumor. In this model, the immune response equation is a non-standard parabolic equation due to the (spatial gradients of diffusible chemicals) of the immune response. The purpose of this paper is to give the numerical methods for solving this kind of free boundary problems. Several simulation results are also given.

Pp. 435-444

Asymptotic Behavior of a Hyperbolic-parabolic Coupled System Arising in Fluid-structure Interaction

Xu Zhang; Enrique Zuazua

In this paper we summarize some recent results on the asymptotic behavior of a linearized model arising in fluid-structure interaction, where a wave and a heat equation evolve in two bounded domains, with natural transmission conditions at the interface. These conditions couple, in particular, the heat unknown with the velocity of the wave solution. First, we show the strong asymptotic stability of solutions. Next, based on the construction of ray-like solutions by means of Geometric Optics expansions and a careful analysis of the transfer of the energy at the interface, we show the lack of uniform decay of solutions in general domains. Finally, we obtain a polynomial decay result for smooth solutions under a suitable geometric assumption guaranteeing that the heat domain envelopes the wave one. The system under consideration may be viewed as an approximate model for the motion of an elastic body immersed in a fluid, which, in its most rigorous modeling should be a nonlinear free boundary problem, with the free boundary being the moving interface between the fluid and the elastic body.

Pp. 445-455