General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source

Saddle points and instability of nonlinear hyperbolic equations

L. E. Payne, D. H. Sattinger · Israel Journal of Mathematics · 1975 · 812 citations

Parabolic Equation, Nonlinear Hyperbolic Equations, Nonlinear Hyperbolic Problem +2

Instability and nonexistence of global solutions to nonlinear wave equations of the form 𝑃𝑢_{𝑡𝑡}=-𝐴𝑢+ℱ(𝓊)

Howard A. Levine · Transactions of the American Mathematical Society · 1974 · 695 citations · Full text

Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms

Vladimir Georgiev, Grozdena Todorova · Journal of Differential Equations · 1994 · 573 citations

Nonlinear Damping, Nonlinear Wave Propagation, Oscillation Theory +5

REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS

J. M. Ball · The Quarterly Journal of Mathematics · 1977 · 518 citations

Lim P, Parabolic Equation, Nonlinear Hyperbolic Problem +5

Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping

Communications in Partial Differential Equations · 1990 · 459 citations

Locally Distributed Damping, Semilinear Wave Equation, Physics +7