The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/840919 |
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| Summary: | 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 (1-∂x2)u0∈M+(R), u0∈H1(R), and u0∈L1(R), the existence and uniqueness of the global weak solution to the equation are shown to be true. |
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| ISSN: | 1085-3375 1687-0409 |