一个弱耗散修正的二分量Dullin-Gottwald-Holm系统解的行为研究

Abstract

Abstract:

In this paper, we consider the Cauchy problem of a weakly dissipative modified two-component Dullin-Gottwald-Holm (mDGH2) system. The local well-posedness and the global existence are analyzed, which is to prove that blow-up phenomena cannot happen under the condition $\left(\|y_{0}\|_{L^{2}}^{2}+\|\rho_{0}\|^{2}_{L^{2}}\right)^{\frac{1}{2}}<\frac{4\lambda} {3}.$ We derive the precise blow-up scenario, and then provide several criteria guaranteeing the blow-up of the solutions to the weakly dissipative mDGH2 system. It is worth noting that the solution to the weakly dissipative system is not affected by the weakly dissipative term.

Key words: Two-component peakon system, Weakly dissipative, Blow-up

CLC Number:

O175.2

Shoufu Tian. On the Behavior of the Solution of a Weakly Dissipative Modified Two-Component Dullin-Gottwald-Holm System[J].Acta mathematica scientia,Series A, 2020, 40(5): 1204-1223.

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References 20

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On the Behavior of the Solution of a Weakly Dissipative Modified Two-Component Dullin-Gottwald-Holm System

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