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

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

Abstract This 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 Schaud...

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Bibliographic Details
Main Authors: Nazlı Irkıl, Khaled Mahdi, Erhan Pişkin, Mohammad Alnegga, Salah Boulaaras
Format: Article
Language:English
Published: SpringerOpen 2023-12-01
Series:Journal of Inequalities and Applications
Subjects:
Blow-up
Dynamical boundary condition
Existence
Logarithmic nonlinearity
Partial differential equations
Mathematical operators
Online Access:https://doi.org/10.1186/s13660-023-03072-3
Description
Summary:Abstract This 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.
ISSN:1029-242X

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