The hyperbolic singular perturbation problem: An operator theoretic approach

DOI10.1016/0022-0396(87)90167-7zbMath0633.35006OpenAlexW2048524859MaRDI QIDQ1096074

Hector O. Fattorini

Publication date: 1987

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(87)90167-7

zbMATH Keywords

convergencesingular perturbationsmall parameterhyperbolicunbounded linear operator

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial value problems for second-order hyperbolic equations (35L15) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20)

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Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Perturbation methods in applied mathematics
• Singular perturbation and boundary layer for an abstract Cauchy problem
• Convergence and approximation theorems for vector values distributions
• Comparison techniques for certain overdamped hyperbolic partial differential equations
• Perturbation theory for cosine families on Banach spaces
• On operator calculus for related partial differential equations
• On the behavior of the solution of the telegraphist's equation for large velocities
• Ordinary differential equations in linear topological spaces. I
• Semigroups and second-order differential equations
• Ordinary differential equations in linear topological space. II
• On the behavior of the solution of the telegraphist's equation for large absorption
• On the Schrödinger Singular Perturbation Problem
• Perturbation of strongly continuous cosine family generators
• Numeric perturbations of evolution equations of parabolic and hyperbolic type
• Equivalent Norms for Sobolev Spaces
• Cauchy problems involving a small parameter
• Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport
• An Asymptotic Analysis of a Certain Hyperbolic Cauchy Problem
• The Identity of Weak and Strong Extensions of Differential Operators
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