Global solutions and finite time blow up for damped semilinear wave equations ☆ ☆The first author was partially supported by the Italian MIUR Project “Calcolo delle Variazioni” while the second author was partially supported by the Italian MIUR Project “Metodi Variazionali e Topologici nello Studio dei Fenomeni Nonlineari” and by the INdAM.

AbstractThis paper is devoted to studying initial value problems for semilinear wave equations with variable coefficients with subcritical exponents for

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On Glassey’s conjecture for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Boundary Value Problems ◽

10.1186/s13661-021-01571-0 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Kimitoshi Tsutaya ◽

Yuta Wakasugi

Keyword(s):

Nonlinear Wave ◽

Finite Time ◽

Wave Equations ◽

Nonlinear Term ◽

Blow Up ◽

Time Derivative ◽

Upper Bounds ◽

Nonlinear Wave Equations ◽

Semilinear Wave Equations

AbstractConsider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime version of Glassey’s conjecture for the time derivative nonlinearity. We also show blow-up results for the space derivative nonlinear term.

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Global existence and finite time blow up for a class of semilinear wave equations on RN

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2015.07.021 ◽

2015 ◽

Vol 70 (6) ◽

pp. 1345-1356 ◽

Cited By ~ 5

Author(s):

Gongwei Liu ◽

Suxia Xia

Keyword(s):

Global Existence ◽

Finite Time ◽

Wave Equations ◽

Blow Up ◽

Semilinear Wave Equations

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On the blow-up of solutions of a convective reaction diffusion equation

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500025828 ◽

1993 ◽

Vol 123 (3) ◽

pp. 433-460 ◽

Cited By ~ 18

Author(s):

J. Aguirre ◽

M. Escobedo

Keyword(s):

Positive Solutions ◽

Finite Time ◽

Blow Up ◽

Global Solutions ◽

Reaction Diffusion ◽

Scalar Function ◽

Reaction Diffusion Equation ◽

Semilinear Parabolic Equation ◽

The Cauchy Problem ◽

Image Position

SynopsisWe study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equationwhere u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time; (b) if 1 < q ≦ p ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.

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