The Kawahara equation in weighted Sobolev spaces
| Autor: | Juan-Ming Yuan, Netra Khanal, Jiahong Wu |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Partial differential equation
Differential equation Applied Mathematics Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics Space (mathematics) Sobolev inequality Sobolev space Initial value problem Uniqueness Korteweg–de Vries equation Mathematical Physics Mathematics |
| Zdroj: | Nonlinearity. 21:1489-1505 |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/0951-7715/21/7/007 |
| Popis: | The initial- and boundary-value problem for the Kawahara equation, a fifth-order KdV type equation, is studied in weighted Sobolev spaces. This functional framework is based on the dual-Petrov–Galerkin algorithm, a numerical method proposed by Shen (2003 SIAM J. Numer. Anal. 41 1595–619) to solve third and higher odd-order partial differential equations. The theory presented here includes the existence and uniqueness of a local mild solution and of a global strong solution in these weighted spaces. If the L2-norm of the initial data is sufficiently small, these solutions decay exponentially in time. Numerical computations are performed to complement the theory. |
| Databáze: | OpenAIRE |
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