Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

Ibrahim, Slim; Lyaghfouri, Abdeslem

doi:10.1051/mmnp/20127206

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Corollary 35 Under the Assumptions Of Lemma 32 We Have1

Blowup In the Case Of Constant Exponents1

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2022

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Cited by 4 publications

(2 citation statements)

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“…for a.e. t ∈ [0, T) because E is an absolutely continuous function (see Georgiev and Todorova 5 ); consequently, H ′ (t) ≥ 0 and 12) for all t in [0, T), by recalling (3.2). We next define…”

Section: Corollary 35 Under the Assumptions Of Lemma 32 We Havementioning

confidence: 99%

Blowup in solutions of a quasilinear wave equation with variable‐exponent nonlinearities

Messaoudi

Talahmeh

2017

Math Methods in App Sciences

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We consider, in this paper, the following nonlinear equation with variable exponents:where a, b > 0 are constants and the exponents of nonlinearity m, p, and r are given functions. We prove a finite-time blow-up result for the solutions with negative initial energy and for certain solutions with positive energy. KEYWORDS blowup, nonlinear damping, Sobolev spaces with variable exponentsA > 0, 0 < < 1. The term Δ r(·) u = div(|∇u| r(·)−2 ∇u) is called r(·)− Laplacian.

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Section: Corollary 35 Under the Assumptions Of Lemma 32 We Havementioning

confidence: 99%

Blowup in solutions of a quasilinear wave equation with variable‐exponent nonlinearities

Messaoudi

Talahmeh

2017

Math Methods in App Sciences

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“…They also discussed the long-time behavior of the solution. Ibrahim and Lyaghfouri [32] considered the following equation…”

Section: Blowup In the Case Of Constant Exponentsmentioning

confidence: 99%

On wave equation: review and recent results

Messaoudi

Talahmeh

2017

Arab. J. Math.

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The aim of this paper is to give an overview of results related to nonlinear wave equations during the last half century. In this regard, we present results concerning existence, decay and blow up for classical nonlinear equations. After that, we discuss briefly some important results of the variable-exponent Lebesgue and Sobolev spaces. Results related to nonexistence and blow up for wave equations with non-standard nonlinearities (nonlinearities involving variable exponents) are given in more detail. Finally, we present some recent decay and blow up results together with their proofs. Mathematics Subject Classification

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Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities

Messaoudi¹,

Al-Smail²,

Talahmeh³

2018

Computers & Mathematics with Applications

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Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

Abstract: Abstract.In this paper, we show finite time blow-up of solutions of the p−wave equation in R N , with critical Sobolev exponent. Our work extends a result by Galaktionov and Pohozaev [4]

Cited by 4 publications

References 8 publications

Blowup in solutions of a quasilinear wave equation with variable‐exponent nonlinearities

Blowup in solutions of a quasilinear wave equation with variable‐exponent nonlinearities

On wave equation: review and recent results

Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities

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