Non-Homogeneous Boundary Value Problems for Linear Dispersive Equations

DOI10.1080/03605302.2011.587492zbMath1246.35048OpenAlexW1987395937MaRDI QIDQ5389568

Corentin Audiard

Publication date: 21 April 2012

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2011.587492

zbMATH Keywords

characteristic polynomialFourier-Laplace transformwell posednessFourier multiplierKreiss symmetrizersDunford-Taylor formulageneralized Kreiss-Lopatinskii condition

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Initial-boundary value problems for linear higher-order PDEs (35G16) Time-dependent Schrödinger equations and Dirac equations (35Q41) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61)

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Cites Work

• Unnamed Item
• Unnamed Item
• Smoothing effect for Schrödinger boundary value problems
• Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension 2. (Existence for an elasto-dynamic nonlinear Neumann problem in two dimensions)
• On nonlinear Schrödinger equations in exterior domains
• Mixed problems for hyperbolic equations. I: Energy inequalities
• Mixed problems for hyperbolic equations. II: Existence theorems with zero initial datas and energy inequalities with initial datas
• A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
• Bilinear virial identities and applications
• A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain
• The Block Structure Condition for Symmetric Hyperbolic Systems
• An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces
• The stability of multidimensional shock fronts
• Weak Stability of Nonuniformly Stable Multidimensional Shocks
• L₂ is a continuable initial condition for kreiss' mixed problems