Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation

By Salim A. Messaoudi. 2006

208 citations recorded by the source corpus.

Abstract In this paper, we consider the nonlinear viscoelastic equation u t t − Δ u + ∫ 0 t g ( t − τ ) Δ u ( τ ) d τ + u t | u t | m − 2 = u | u | p − 2 with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p > m , we prove that there are solutions with positive initial energy that blow up in finite time.

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

View Paper: https://www.semanticscholar.org/paper/0262fe12d775df4fdf8610481f4f4bf1dc20465e

Citations in the corpus

• Blow‐up of solutions for a viscoelastic wave equation with variable exponents (2019, unknown): “Using (4), (7), (9), (10), and (26), we find that for 0 < λ(t) ≤ B−1 1 , E(t) ≥ 1 2 ( 1 − ∫ t”