Radius of analyticity and exponential convergence for spectral projections of the generalized KdV equation

Bjørkavåg, Magnar; Kalisch, Henrik

doi:10.1016/j.cnsns.2009.05.015

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…Although there exist results in the literature treating particular models, cf. [7,9,29], we are not aware of similar results for general semilinear hyperbolic systems on R d . In the present paper we consider systems with initial data analytic on R d and admitting a holomorphic extension in a strip of the form {x + iy : |y| < ε 0 } for some ε 0 > 0.…”

Section: Introductionmentioning

confidence: 97%

On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

Cappiello

D’Ancona

Nicola

2014

Journal of Differential Equations

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Abstract. We study the problem of propagation of analytic regularity for semilinear symmetric hyperbolic systems. We adopt a global perspective and we prove that if the initial datum extends to a holomorphic function in a strip of radius (=width) ε 0 , the same happens for the solution u(t, ·) for a certain radius ε(t), as long as the solution exists. Our focus is on precise lower bounds on the spatial radius of analyticity ε(t) as t grows.We also get similar results for the Schrödinger equation with a real-analytic electromagnetic potential.

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Section: Introductionmentioning

confidence: 97%

On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

Cappiello

D’Ancona

Nicola

2014

Journal of Differential Equations

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On the study the radius of analyticity for Korteweg-de-Vries type systems with a weakly damping

Otmani,

Bouharou,

Zennir

et al. 2024

MATH

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<p>In the present paper, we considered a Korteweg-de Vries type system with weakly damping terms and initial data in the analytic Gevery spaces. The presence of tow functions $ c_1(x), c_2(x) $, called damping coefficients, made the system more interesting from an application point of view due to their great importance in physics. To start, by using the fixed point theorem in Banach space, we investigated the local well-posedness. Additionally, by employing an approximate conservation law, we extended this to be global in time, ensuring that the radius of analyticity of solutions remained uniformly bounded below by a fixed positive number for all time.</p>

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Radius of analyticity and exponential convergence for spectral projections of the generalized KdV equation

Cited by 2 publications

References 24 publications

On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

On the study the radius of analyticity for Korteweg-de-Vries type systems with a weakly damping

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