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- W2002189239 abstract "A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msubsup><mml:mrow><mml:mo>∂</mml:mo></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>)</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>),</mml:mo></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:math>, the existence and uniqueness of the global weak solution to the equation are shown to be true." @default.
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- W2002189239 date "2012-01-01" @default.
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- W2002189239 title "The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term" @default.
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- W2002189239 doi "https://doi.org/10.1155/2012/840919" @default.
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