2019/01/09 by Barbara Kaltenbacher, Kaltenbacher, Barbara, Vanja Nikolić +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #35L72 #35L77 #35L80 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1901.02795
openalex publication_date 2019/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the Jordan-Moore-Gibson-Thompson equation, a third\norder in time wave equation describing the nonlinear propagation of sound that\navoids the infinite signal speed paradox of classical second order in time\nstrongly damped models of nonlinear acoustics, such as the Westervelt and the\nKuznetsov equation. We show well-posedness in an acoustic velocity potential\nformulation with and without gradient nonlinearity, corresponding to the\nKuznetsov and the Westervelt nonlinearities, respectively. Moreover, we\nconsider the limit as the parameter of the third order time derivative that\nplays the role of a relaxation time tends to zero, which again leads to the\nclassical Kuznetsov and Westervelt models. To this end, we establish\nappropriate energy estimates for the linearized equations and employ\nfixed-point arguments for well-posedness of the nonlinear equations. The\ntheoretical results are illustrated by numerical experiments.\n