On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up

Author:

Irkıl Nazlı,Mahdi Khaled,Pişkin Erhan,Alnegga Mohammad,Boulaaras Salah

Abstract

AbstractThis paper deals with a hyperbolic-type equation with a logarithmic source term and dynamic boundary condition. Given convenient initial data, we obtained the local existence of a weak solution. Local existence results of solutions are obtained using the Faedo-Galerkin method and the Schauder fixed-point theorem. Additionally, under suitable assumptions on initial data, the lower bound time of the blow-up result is investigated.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference36 articles.

1. Adams, R.A., Fournier, J.J.F.: Sobolev Spaces. Academic Press, New York (2003)

2. Bejenaru, I., Diaz, J.I., Vrabie, I.I.: An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions. Electron. J. Differ. Equ. 2001, 50 (2001)

3. Beylin, A.B., Pulkina, L.S.: A problem with dynamical boundary condition for a one-dimensional hyperbolic equation. J. Samara State Tech. Univ., Ser. Phys. Math. Sci. 24(3), 407–423 (2020). https://doi.org/10.14498/vsgtu1775

4. Bialynicki-Birula, I., Mycielski, J.: Wave equations with logarithmic nonlinearities. Bull. Pol. Acad. Sci. 3(23), 461–466 (1975)

5. Bialynicki-Birula, I., Mycielski, J.: Nonlinear wave mechanics. Ann. Phys. 100(1–2), 62–93 (1976). https://doi.org/10.1016/0003-4916(76)90057-9

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