Blow up, growth, and decay of solutions for a class of coupled nonlinear viscoelastic Kirchhoff equations with distributed delay and variable exponents

Abstract

Abstract In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 $f_{1}=f_{2}=0$ .

Keywords

• Viscoelastic equation
• Partial differential equations
• Blow up
• Exponential growth
• General decay
• Distributed delay term