Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

By Huafei Di, Y. Shang, Zefang Song. 2020

64 citations recorded by the source corpus.

Abstract This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity u t t − Δ u − Δ u t = φ p ( u ) log | u | in a bounded domain Ω ⊂ R n . We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26ab62ccb6a2b2e40f4a779ad2254b42afb14fa5

Citations in the corpus

• Blow-up phenomena for a viscoelastic wave equation with strong damping and logarithmic nonlinearity (2020, unknown): “3) in the present work by applying the ideas in [11, 18].”