Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping

Cavalcanti, Marcelo M.; Cavalcanti, V. N. Domingos; Komornik, Vilmos; Rodrigues, José Henrique

doi:10.1016/j.anihpc.2013.08.003

Cited by 22 publications

(20 citation statements)

References 21 publications

(22 reference statements)

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“…We define Proof. The same result was obtained for the generalized KdV and the KdV-Burgers equations in [19] and [7], respectively. Since the proof is analogous and follows from classical arguments we omit it.…”

Section: Case 1 ≤ P <supporting

confidence: 80%

On the well-posedness and asymptotic behaviour of the generalized Korteweg–de Vries–Burgers equation

Gallego¹,

Pazoto²

2018

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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In this paper we are concerned with the well-posedness and the exponential stabilization of the generalized Korteweg-de Vries Burgers equation, posed on the whole real line, under the effect of a damping term. Both problems are investigated when the exponent p in the nonlinear term ranges over the interval [1,5). We first prove the global well-posedness in H s (R), for 0 ≤ s ≤ 3 and 1 ≤ p < 2, and in H 3 (R), when p ≥ 2. For 2 ≤ p < 5, we prove the existence of global solutions in the L 2 -setting. Then, by using multiplier techniques combined with interpolation theory, the exponential stabilization is obtained for a indefinite damping term and 1 ≤ p < 2 . Under the effect of a localized damping term the result is obtained when 2 ≤ p < 5. Combining multiplier techniques and compactness arguments it is shown that the problem of exponential decay is reduced to prove the unique continuation property of weak solutions

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Section: Case 1 ≤ P <supporting

confidence: 80%

On the well-posedness and asymptotic behaviour of the generalized Korteweg–de Vries–Burgers equation

Gallego¹,

Pazoto²

2018

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…Compare this result with the one-dimensional case from [4] (in fact, the present paper is inspired by that one), where the initial value problem is considered for damped Korteweg-de Vries-Burgers equation…”

Section: Introduction Description Of Main Resultsmentioning

confidence: 68%

An initial–boundary value problem in a strip for two-dimensional Zakharov–Kuznetsov–Burgers equation

Faminskii

2015

Nonlinear Analysis: Theory, Methods & Applications

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“…We are concerned with an initial-boundary value problem (IBVP) for the two-dimensional Zakharov-Kuznetsov-Burgers (ZKB) equation which includes dissipation and dispersion and has been studied by various researchers due to its applications in Mechanics and Physics [1,2,3]. One can find extensive bibliography and sharp results on decay rates of solutions to the Cauchy problem (IVP) for (1.2) in [1].…”

Section: Introductionmentioning

confidence: 99%

The 2D Zakharov-Kuznetsov-Burgers equation on a strip

Larkin

2016

bspm

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An initial-boundary value problem for the 2D Zakharov-KuznetsovBurgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in the L 2 -norm.

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Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping

Abstract: We consider the KdV-Burgers equation u t + u xxx − u xx + λu + uu x = 0 and its linearized version u t + u xxx − u xx + λu = 0 on the whole real line. We investigate their well-posedness their exponential stability when λ is an indefinite damping.

Cited by 22 publications

References 21 publications

On the well-posedness and asymptotic behaviour of the generalized Korteweg–de Vries–Burgers equation

On the well-posedness and asymptotic behaviour of the generalized Korteweg–de Vries–Burgers equation

An initial–boundary value problem in a strip for two-dimensional Zakharov–Kuznetsov–Burgers equation

The 2D Zakharov-Kuznetsov-Burgers equation on a strip

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