# The 2D Kawahara Equation on a Half-Strip

The 2D Kawahara Equation on a Half-Strip We formulate on a half-strip an initial boundary value problem for the two-dimensional Kawahara equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the elevated norm \begin{aligned} \Vert u\Vert ^2_{H^1(D)}(t)+\Vert u_{xx}\Vert ^2_{L^2(D)}(t) \end{aligned} ‖ u ‖ H 1 ( D ) 2 ( t ) + ‖ u x x ‖ L 2 ( D ) 2 ( t ) of small solutions as $$t \rightarrow \infty$$ t → ∞ are proven. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# The 2D Kawahara Equation on a Half-Strip

, Volume 70 (3) – Dec 1, 2014
26 pages

/lp/springer_journal/the-2d-kawahara-equation-on-a-half-strip-fv0TGlEceN
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9246-4
Publisher site
See Article on Publisher Site

### Abstract

We formulate on a half-strip an initial boundary value problem for the two-dimensional Kawahara equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the elevated norm \begin{aligned} \Vert u\Vert ^2_{H^1(D)}(t)+\Vert u_{xx}\Vert ^2_{L^2(D)}(t) \end{aligned} ‖ u ‖ H 1 ( D ) 2 ( t ) + ‖ u x x ‖ L 2 ( D ) 2 ( t ) of small solutions as $$t \rightarrow \infty$$ t → ∞ are proven.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2014

### References

• The Korteweg-de Vries- Kawahara equation in a bounded domain and some numerical results
Ceballos, J; Sepulveda, M; Villagran, O
• Well-posedness and scattering results for the generalized Korteweg-de Vries equation and the contraction principle
Kenig, CE; Ponce, G; Vega, L

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