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

Anne Boutet de Monvel; Dmitry Shepelsky

Displaying similar documents to “Initial boundary value problem for the mKdV equation on a finite interval”

A spectral characterization of the behavior of discrete time AR–representations over a finite time interval

E. N. Antoniou, Antonis I. G. Vardulakis, Nikolas P. Karampetakis (1998)

Kybernetika

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In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.

Falseness of the finiteness property of the spectral subradius

Adam Czornik, Piotr Jurgas (2007)

International Journal of Applied Mathematics and Computer Science

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We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but...

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

Fokas, A.S., Kamvissis, S. (2004)

Abstract and Applied Analysis

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The Direct and Inverse Spectral Problems for some Banded Matrices

Zagorodnyuk, S. M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.

Spectral sets and the Drazin inverse with applications to second order differential equations

Trung Dinh Tran (2002)

Applications of Mathematics

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The paper defines and studies the Drazin inverse for a closed linear operator $A$ in a Banach space $X$ in the case that $0$ belongs to a spectral set of the spectrum of $A$ . Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space.

On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball

Nikolai Nikolov, Pascal J. Thomas (2008)

Annales Polonici Mathematici

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Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone $C_{A}$ to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.

A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem

Jamel Ben Amara (2011)

Colloquium Mathematicae

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We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string. ...

Long time asymptotics of the Camassa–Holm equation on the half-line

Anne Boutet de Monvel, Dmitry Shepelsky (2009)

Annales de l’institut Fourier

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We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation $u_{t} - u_{t x x} + 2 u_{x} + 3 u u_{x} = 2 u_{x} u_{x x} + u u_{x x x}$ on the half-line $x \geq 0$ . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane $x > 0$ , $t > 0$ having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of...