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. Applied Mathematics and Optimization Springer Journals

The 2D Kawahara Equation on a Half-Strip

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Springer US
Copyright © 2014 by Springer Science+Business Media New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
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