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The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation

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  • Meng Wu

Abstract

The existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space C([0, T); Hs(R)) ∩C1([0, T); Hs−1(R)) provided that the initial value lies in Hs(R) with s > 3/2. Meanwhile, we prove the existence of global weak solutions in L∞([0, ∞); L2(R)) for the equation.

Suggested Citation

  • Meng Wu, 2013. "The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:619068
    DOI: 10.1155/2013/619068
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    References listed on IDEAS

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    1. Shaoyong Lai, 2013. "The Global Weak Solution for a Generalized Camassa-Holm Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, January.
    2. Shaoyong Lai, 2013. "The Global Weak Solution for a Generalized Camassa‐Holm Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Haibo Yan & Ls Yong, 2014. "The Local Stability of Solutions for a Nonlinear Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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