Local Existence and Blow Up of Solutions for a System of Viscoelastic Wave Equations of Kirchhoff Type with Delay and Logarithmic Nonlinearity

Subject Areas : International Journal of Mathematical Modelling & Computations

Mahammad Khuddush ¹ , Kapula Rajendra Prasad ² , Bharathi Botta ³

1 - Department of Applied Mathematics Andhra University Visakhapatnam India-530003
2 - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, India
3 - Department of Applied Mathematics Andhra University Visakhapatnam India-530003

Received: 2020-09-29 Accepted : 2021-03-04 Published : 2021-09-01

Keywords: Delay, Wave Equation, Local existence, blow up, logarithmic nonlinearity,

Abstract :

In this paper, we consider a system of viscoelastic wave equations of Kirchhoff type with delay and logarithmic nonlinearity. We obtain the local existence of solution by using the Faed-Galerkin approximation and under suitable conditions, we prove the blow up of solutions in finite time.