Global nonexistence of solutions for a system of nonlinear viscoelastic wave equations with degenerate damping and source terms

A finite‐time blow‐up result for a class of solutions with positive initial energy for coupled system of heat equations with memories

“…In fact,we adapt the method introduced by Li and Xie and Fujita and developed later by Benaissa et al, Ouchenane et al, and Zennir. ()…”

Nonexistence of Global Solutions for Coupled System of Pseudoparabolic Equations with Variable Exponents and Weak Memories

“…System (1), where the exponents qðxÞ = q and pðxÞ = p, the existence/nonexistence results have been extensively studied (please see [11][12][13][14][15]).…”

“…Journal of Function Spaces Theorem 8. Assume that (10), (12), and (14) hold. Then, the problem (1)-(4) has a unique local solution ðw, zÞ satisfying…”

“…Lemma 10. Let ðw, zÞ be the solution of (1)-(4) with (10)- (14). Then, the energy functional satisfies…”

“…Proof. Multiplying (1) 1 by ∂ t w and (1) 2 by ∂ t z, integrating by parts over Ω, summing and using (14) and Lemma 6. Then, it is clear that f 1 ðw, zÞ and f 2 ðw, zÞ are bounded, so the potential Fðw, zÞ exists and is given by (85) as follows…”