Improvement on the blow-up of the wave equation with the scale-invariant damping and combined nonlinearities

Hamouda, Makram; Hamza, Mohamed Ali

doi:10.1016/j.nonrwa.2020.103275

Cited by 24 publications

(22 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the equation (1.10) is somehow related to the Euler-Darboux-Poisson equation. Moreover, thanks to this transformation, which implies a kind of similarity with the scale-invariant damping case, we can inherit the methods used in our previous works [4,5,6] to build the proofs of our main results which are related, as a first target, to the blow-up of the solution of (1.1) and, as a secondary aim, to the blow-up of (1.7).…”

Section: Introductionmentioning

confidence: 99%

Blow-up and lifespan estimate for the generalized Tricomi equation with mixed nonlinearities

Hamouda¹,

Hamza²

2021

APAM

Self Cite

View full text Add to dashboard Cite

We study in this article the blow-up of the solution of the generalized Tricomi equation in the presence of two mixed nonlinearities, namely we considerwith small initial data, where m ≥ 0.For the problem (T r) with m = 0, which corresponds to the uniform wave speed of propagation, it is known that the presence of mixed nonlinearities generates a new blow-up region in comparison with the case of a one nonlinearity (|u t | p or |u| q ). We show in the present work that the competition between the two nonlinearities still yields a new blow region for the Tricomi equation (T r) with m ≥ 0, and we derive an estimate of the lifespan in terms of the Tricomi parameter m. As an application of the method developed for the study of the equation (T r) we obtain with a different approach the same blow-up result as in [18] when we consider only one time-derivative nonlinearity, namely we keep only |u t | p in the right-hand side of (T r).

show abstract

Section: Introductionmentioning

confidence: 99%

Blow-up and lifespan estimate for the generalized Tricomi equation with mixed nonlinearities

Hamouda¹,

Hamza²

2021

APAM

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the case α = 0 and μ ≥ 0, it has been recently shown by Hamouda and Hamza [16] that blow-up in finite time occurs and the lifespan of the blow-up solutions satisfies…”

Section: Introductionmentioning

confidence: 99%

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

Tsutaya

Wakasugi

2021

Bound Value Probl

View full text Add to dashboard Cite

show abstract

“…The damped semilinear wave equation

({, \begin{matrix} left \\ array u_{t t} - Δ u + \frac{μ}{{(1 + t)}^{β}} u_{t} = f (u, u_{t}), t > 0, x \in ℝ^{n}, \\ array (u, u_{t}) (x, 0) = (ε u_{0} (x), ε u_{1} (x)), x \in ℝ^{n} \end{matrix})

has been studied extensively in recent years, where

\frac{μ}{{false(1 + t false)}^{β}} u_{t} false(β \in ℝ false)

is the damping term (see detailed illustration in previous works 24–40 ). Lai and Tu 36 consider the blow‐up dynamic and lifespan estimate of solution to semilinear wave equation with

f false(u, u_{t} false) = false| u {false|}^{p}, false| u_{t} {false|}^{p}

and damping term

\frac{μ}{{false(1 + false| x false| false)}^{β}} u_{t} false(β > 2 false)

by using test function approach, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Lai et al 41 study the upper bound lifespan estimate of solution to semilinear wave equation with scale invariant damping term and mass term by employing the Kato lemma and iteration argument. Upper bound lifespan estimate of solution to problem () with

f false(u, u_{t} false) = false| u_{t} {false|}^{p} + false| u {false|}^{q}

and scale invariant damping is analyzed in Hamouda and Hamza 28,29 . Ming et al 38 establish lifespan estimate of solution to variable coefficient wave equation with divergence form nonlinearity in the subcritical and critical cases by employing rescaled test function method and iteration technique.…”

Section: Introductionmentioning

confidence: 99%

Blow‐up and lifespan estimates of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations

Ming

Yang

Fan

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

This work is devoted to investigating formation of singularities of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations with power nonlinearities |v|p, |u|q, derivative nonlinearities |vt|p, |ut|q, mixed nonlinearities |v|q, |ut|p, and combined nonlinearities false|vtfalse|p1+false|vfalse|q1,0.1emfalse|utfalse|p2+false|ufalse|q2, respectively. Upper bound lifespan estimates of solutions to the problem in the subcritical and critical cases are also established. The main tool employed in the proofs is test function technique. The novelty is that lifespan estimates of solutions are connected with the well‐known Strauss exponent and Glassey exponent.

show abstract

Improvement on the blow-up of the wave equation with the scale-invariant damping and combined nonlinearities

Cited by 24 publications

References 27 publications

Blow-up and lifespan estimate for the generalized Tricomi equation with mixed nonlinearities

Blow-up and lifespan estimate for the generalized Tricomi equation with mixed nonlinearities

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

Blow‐up and lifespan estimates of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations

Contact Info

Product

Resources

About