Asymptotic stability of solutions to quasilinear hyperbolic equations with variable sources

Li, Xiaolei; Guo, Bao‐Zhu; Liao, Menglan

doi:10.1016/j.camwa.2019.08.016

Cited by 23 publications

(15 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Obviously, Theorem 4.1 implies that the solution u is global. We borrow some ideas from [22,6,18]. Multiplying (1.1) by u and integrating over Ω × (s, T ) with s < T yield…”

Section: Global Existence and Energy Decay Estimatesmentioning

confidence: 99%

On behavior of solutions to a Petrovsky equation with damping and variable-exponent source

Liao,

Tan

2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper deals with the following Petrovsky equation with damping and nonlinear source−2 u under initial-boundary value conditions, where M (s) = a + bs γ is a positive C 1 function with parameters a > 0, b > 0, γ ≥ 1, and m(x), p(x) are given measurable functions. The upper bound of the blow-up time is derived for low initial energy using the differential inequality technique. For m(x) ≡ 2, in particular, the upper bound of the blow-up time is obtained by the combination of Levine's concavity method and some differential inequalities under high initial energy. In addition, by making full use of the strong damping, the lower bound of the blow-up time is discussed. Moreover, the global existence of solutions and an energy decay estimate are presented by establishing some energy estimates and by exploiting a key integral inequality.

show abstract

“…Obviously, Theorem 4.1 implies that the solution u is global. We borrow some ideas from [22,6,18]. Multiplying (1.1) by u and integrating over Ω × (s, T ) with s < T yield…”

Section: Global Existence and Energy Decay Estimatesmentioning

confidence: 99%

On behavior of solutions to a Petrovsky equation with damping and variable-exponent source

Liao,

Tan

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let us set µ = µ 0 + µ 1 . Choosing δ 1 , δ 2 , δ 3 > 0 sufficiently small and µ 1 > 0 sufficiently large, from (27), it follows that…”

Section: Proof Of Main Theoremsmentioning

confidence: 99%

Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

Buhrii

Kholyavka

Пукач

et al. 2020

Carpathian Math. Publ.

View full text Add to dashboard Cite

show abstract

“…On the other hand, recently, researchers have much interested in the study of nonlinear models of elliptic, parabolic, and hyperbolic equations with variable exponent nonlinearities 9–15 . Messaoudi et al 13 considered the nonlinear damped equation

w_{t t} - d i v (| \nabla w |^{r (x) - 2} \nabla w) + | w_{t} |^{γ (x) - 2} w_{t} = 0 .

Under appropriate conditions on the initial data and the exponents r (·), γ (·), they showed the decay estimates applying the multiplier method.…”

Section: Introductionmentioning

confidence: 99%

Existence and decay results for a von Karman equation with variable exponent nonlinearities

Park

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, we consider a von Karman equation with variable exponent nonlinearities wtt(x,t)+Δ2w(x,t)+|wt(x,t)|γ(x)−2wt(x,t)=[w(x,t),F(w(x,t))]+|w(x,t)|p(x)−2w(x,t) in a bounded domain normalΩ⊂ℝ2. We firstly discuss an existence result of solutions by utilizing Faedo‐Galerkin approximation technique. Then, we undertake an investigation of asymptotic stability to the solutions by making use of the multiplier method.

show abstract

Asymptotic stability of solutions to quasilinear hyperbolic equations with variable sources

Cited by 23 publications

References 25 publications

On behavior of solutions to a Petrovsky equation with damping and variable-exponent source

On behavior of solutions to a Petrovsky equation with damping and variable-exponent source

Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

Existence and decay results for a von Karman equation with variable exponent nonlinearities

Contact Info

Product

Resources

About