Zero-dispersion limit for integrable equations on the half-line with linearisable data.

Fokas, A.S.; Kamvissis, S.

Displaying similar documents to “Zero-dispersion limit for integrable equations on the half-line with linearisable data.”

On a mixed boundary values problem for Lavrentev type equations

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Initial boundary value problem for the mKdV equation on a finite interval

Anne Boutet de Monvel, Dmitry Shepelsky (2004)

Annales de l’institut Fourier

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We analyse an initial-boundary value problem for the mKdV equation on a finite interval $(0, L)$ by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex $k$ -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at $t = 0$ and $x = 0, L$ . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms...

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Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

Yoshihiro Shibata (1993)

Commentationes Mathematicae Universitatis Carolinae

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The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.