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arXiv · 2404.03920

Global existence and asymptotic behavior of the Westervelt--hyperbolic Pennes system

Imen Benabbas·Belkacem Said-Houari
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Abstract

In this work, we investigate the global existence and asymptotic behavior of 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). First, we prove that the solution exists globally in time, provided that the lower-order Sobolev norms of the initial data are considered to be small, while the higher-order norms can be arbitrarily large. This is done using a continuity argument together with some interpolation inequalities. Second, we prove an exponential decay of the solution under the same smallness assumptions on the initial data.

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Imen Benabbas, Belkacem Said-Houari. 2024-04-05. Global existence and asymptotic behavior of the Westervelt--hyperbolic Pennes system. https://arxiv.org/abs/2404.03920

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