An inverse problem for Moore–Gibson–Thompson equation arising in high intensity ultrasound
Rogelio ArancibiaDepartamento de Matemática , Universidad Técnica Federico Santa María , Casilla 110-V , Valparaíso , ChileRodrigo LecarosDepartamento de Matemática , Universidad Técnica Federico Santa María , Casilla 110-V , Valparaíso , ChileAlberto MercadoDepartamento de Matemática , Universidad Técnica Federico Santa María , Casilla 110-V , Valparaíso , ChileSebastián ZamoranoDepartamento de Matemática y Ciencia de la Computación , Facultad de Ciencia , Universidad de Santiago de Chile (USACH) , Casilla 307, Correo 2 , Santiago , Chile
2022en
ABI
Annotatsiya
Abstract In this article, we study the inverse problem of recovering a space-dependent coefficient of the Moore–Gibson–Thompson (MGT) equation from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz stability for this inverse problem, and we design a convergent algorithm for the reconstruction of the unknown coefficient. The techniques used are based on Carleman inequalities for wave equations and properties of the MGT equation.
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