Infinite propagation speed for the Degasperis–Procesi equation

Henry, David

doi:10.1016/j.jmaa.2005.03.001

Cited by 78 publications

(50 citation statements)

References 21 publications

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“…Matsuno [36] studied multisoliton solutions and their peakon limits. Analogous to the case of Camassa-Holm equation [8], Henry [25] showed that smooth solutions to Eq. (1.2) have infinite speed of propagation.…”

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confidence: 94%

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Initial boundary value problems of the Degasperis-Procesi equation

Escher

Yin

2008

Parabolic and Navier–Stokes Equations

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Abstract. We mainly study initial boundary value problems for the Degasperis-Procesi equation on the half line and on a compact interval. By the symmetry of the equation, we can convert these boundary value problems into Cauchy problems on the line and on the circle, respectively. Applying thus known results for the equation on the line and on the circle, we first obtain the local well-posedness of the initial boundary value problems. Then we present some blow-up and global existence results for strong solutions. Finally we investigate global and local weak solutions on the half line and on a compact interval, respectively. One interesting result is that the corresponding strong solution to the Degasperis-Procesi equation on the half line blows up in finite time provided the initial potential, assumed nonpositive, is not identically zero. Another one is that all global strong solutions to the Degasperis-Procesi equation on a compact interval blow up in finite time.2000 Mathematics Subject Classification: 35G25, 35L05. Key words and phrases: Degasperis-Procesi equation, initial boundary value problems, local well-posedness, blow-up and global existence, global and local weak solutions.

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confidence: 94%

“…[5,25,30,31,32,36,44,45,46,47] and the citations therein. For example, Yin proved local well-posedness of Eq.…”

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confidence: 99%

Initial boundary value problems of the Degasperis-Procesi equation

Escher

Yin

2008

Parabolic and Navier–Stokes Equations

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“…Important contributions to the study of the DP equation were also made by Matsuno and Henry et al (see e.g. [13,31]). …”

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confidence: 99%

Perturbational self-similar solutions for the 2-component Degasperis--Procesi system via a characteristic method

An¹,

Cheung²,

Yuen³

2016

Turk J Math

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In this paper, the two-component Degasperis-Procesi system arising in shallow water theory is investigated.By using a special transformation and the characteristic method, a class of perturbational self-similar solutions is constructed. Such solutions are not only more general than those obtained by Yuen in 2011, but also they may have potential applications in the modeling of tsunamis. In addition, the method proposed can be extended to other mathematical physics models like the two-component Camassa-Holm equations.

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“…Matsuno [48] studied multisoliton solutions and their peakon limits. Analogous to the case of the Camassa-Holm equation [11,35], Henry [34] showed that smooth solutions to the Degasperis-Procesi equation have infinite speed of propagation (see also [49]). Coclite and Karlsen [9] also obtained global existence results for entropy weak solutions in the class of L 1 (R) ∩ BV (R) and the class of…”

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confidence: 98%

“…Since the Degasperis-Procesi equation was derived, many papers were devoted to its study; cf. [9,31,34,42,44,45,46,47,48,55] and the citations therein. For example, Yin proved local well-posedness to (1.5) with initial data u 0 ∈ H s , s > 3 2 on the line [55] and the precise blow-up scenario and a blow-up result were derived.…”

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confidence: 99%