References
- Hamilton MF, Blackstock DT. Nonlinear acoustics. New York (NY): Academic Press; 1997.
- Kaltenbacher M. Numerical simulations of mechatronic sensors and actuators. Berlin: Springer; 2004.
- Westervelt PJ. Parametric acoustic array. J. Acoust. Soc. Am. 1963;35:535–537.
- Kaltenbacher B, Lasiecka I. Global existence and exponential decay rates for the Westervelt equation. Discrete Continuous Dyn. Syst. Ser. S. 2009;2:503–525.
- Kaltenbacher B, Lasiecka I, Veljovi S. Well-posedness and exponential decay for the Westervelt equation with inhomogeneous Dirichlet boundary data. Vol. 60, In: Escher J, editor. Progress in nonlinear differential equations and their applications. Basel: Birkhaeuser; 2011. p. 357–387.
- Brunnhuber R, Kaltenbacher B, Radu P. Relaxation of regularity for the Westervelt equation by nonlinear damping with application in acoustic--acoustic and elastic--acoustic coupling. Evol. Equ. Control Theory. 2014;34:595–626.
- Nikolić V. Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions. J. Math. Anal. Appl. 2015;427:1131–1167.
- Bamberger A, Glowinski R, Tran QH. A domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change. SIAM J. Numer. Anal. 1997;34:603–639.
- Lindqvist P. Notes on the p-Laplace equation. Lecture notes. Jyväskylä: University of Jyväskylä; 2006.
- Ural NN. Degenerate quasilinear elliptic systems. Zap. Na. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI). 1968;7:184–222.
- DiBenedetto E. Degenerate parabolic equations. Universitext. New York (NY): Springer-Verlag; 1993. xv 387.
- DiBendetto E, Friedman A. Regularity of solutions of nonlinear degenerate parabolic systems. J. für die reine und angew. Math. 1984;349:83–128.
- Wilstein Z. Global well-posedness for a nonlinear wave equation with p-Laplacian damping [PhD thesis]. Lincoln: University of Nebraska-Lincoln; 2011.
- Gao H, Ma TF. Global solutions for a nonlinear wave equation with the {\it p}-Laplacian operator. Electron. J. Qualitative Theory Differ. Equ. 1999;11:1–13.
- Nikoli V, Kaltenbacher B. Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy. Forthcoming. arXiv:1506.02781 [math.OC].
- Evans LC. Partial differential equations. 2nd ed. Providence: American Mathematical Society; 1998.
- Liu W, Yan N. Quasi-norm local error estimators for {\it p}-Laplacian. SIAM J. Numer. Anal. 2002;39:100–127.
- Bojarski B, Iwaniec T. {\it p}-harmonic equation and quasiregular mappings. Partial Differ. Equ. Banach Center Publ. 1987;19:25–38.
- Ammari H, Chen D, Zou J. Well-posedness of a pulsed electric field model in biological media and its finite element approximation. arXiv:1502.06803v2 [math.AP]; 2015.
- Delfour MC, Zolesio JP. Shapes and geometries. 2nd ed. Philadelphia (PA): SIAM; 2001.