On higher regularity for the Westervelt equation with strong nonlinear damping. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: Nikolić, Vanja; Kaltenbacher, Barbara
• Is Part Of: Applicable analysis. Volume 95:Issue 12(2016)
• Page Start: 2824
• Page End: 2840
• Publication Date: 2016-12-01
• Subjects: Nonlinear acoustics -- interface coupling -- Westervelt's equation -- q-Laplacian; 35L05 -- 35L20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1114607
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We show higher interior regularity for the Westervelt equation with strong nonlinear damping term of q -Laplace type. Secondly, we investigate an interface coupling problem for these models, which arise, e.g. in the context of medical applications of high intensity focused ultrasound in the treatment of kidney stones. We show that the solution to the coupled problem exhibits piecewise regularity in space, provided that the gradient of the acoustic pressure is essentially bounded in space and time on the whole domain. This result is of importance in numerical approximations of the present problem as well as in gradient based algorithms for finding the optimal shape of a focusing acoustic lens in lithotripsy.