Blow-up and critical exponents for nonlinear hyperbolic equations

60 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source (2009, background): “See, for instance the followingworks: [1,5,7–12,14–16,18–20,25–32,34–36] and a long list of references therein.”
Wave Equation with p(x,t) - Laplacian and Damping Term: Existence and Blow-up (2011, background): “Here we follow the paper [19], where the authors proved the blow up for an abstract hyperbolic equation in a Banach space which includes, as an example, the equation of the type (1) with the a = b = 1, p = const.”
Blowup in solutions of a quasilinear wave equation with variable‐exponent nonlinearities (2017, result): “Under appropriate assumptions on the initial data, they proved the finite-time blowup of solutions and, hence, extended a result by Galaktionov and Pohozaev.13 Wu and Xue14 studied the following quasilinear hyperbolic equation: utt − 𝜓(t) div (|∇ut|p−2∇ut) − n∑ i=1 𝜕 𝜕xi 𝜎i(uxi) + 𝜇|ut|𝛼ut = 0”