Global Existence and Finite Time Blow-Up in a New Class of Non-Linear Viscoelastic Wave Equation - Zakia, Tebba; Degaichia, Hakima; Messaoudene, Hadia (Discontinuity, Nonlinearity, and Complexity, 2026)
A new class of nonlinear viscoelastic wave equation is studied. Under appropriate conditions imposed on h, the global existence of solutions with any initial data is proved when $m≥ p$, and a finite time blow-up with negative initial energy is obtained when $p>m$.