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The Westervelt--Pennes--Cattaneo model: local well-posedness and singular limit for vanishing relaxation time

The Westervelt--Pennes--Cattaneo model: local well-posedness and singular limit for vanishing relaxation time

Authors :
Benabbas, Imen
Said-Houari, Belkacem
Publication Year :
2023

Abstract

In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on a coupled system of the Westervelt equation and the hyperbolic Pennes bioheat equation (Westervelt--Pennes--Cattaneo model). Using the energy method together with a fixed point argument, we prove that our model is locally well-posed and does not degenerate under a smallness assumption on the pressure data in the Westervelt equation. In addition, we perform a singular limit analysis and show that the Westervelt--Pennes--Fourier model can be seen as an approximation of the Westervelt--Pennes--Cattaneo model as the relaxation parameter tends to zero. This is done by deriving uniform bounds of the solution with respect to the relaxation parameter.

Subjects

Subjects :
Mathematics - Analysis of PDEs

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2304.02881
Document Type :
Working Paper