Criterion for the solvability of the weighted Cauchy problem for an abstract Euler-Poisson-Darboux equation

DOI10.1134/S0012266118050063zbMath1403.34043OpenAlexW4252671470WikidataQ115250758 ScholiaQ115250758MaRDI QIDQ1660876

A. V. Glushak

Publication date: 16 August 2018

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

Full work available at URL: https://doi.org/10.1134/s0012266118050063

zbMATH Keywords

generatorresolventEuler-Poisson-Darboux equationuniform well-posednessoperator Bessel functionsweighted abstract Cauchy problem

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Linear differential equations in abstract spaces (34G10)

Related Items (7)

On the solvability of nonlocal initial-boundary value problems for a partial differential equation of high even order ⋮ On the relationship between the solutions of an abstract Euler-Poisson-Darboux equation and fractional powers of the operator coefficient in the equation ⋮ A family of singular differential equations ⋮ Transmutation Operators as a Solvability Concept of Abstract Singular Equations ⋮ Solvability of degenerating hyperbolic differential equations with unbounded operator coefficients ⋮ An operator formula for the shift of the solution of the Cauchy problem for an abstract Euler-Poisson-Darboux equation ⋮ Uniqueness criterion for solutions of nonlocal problems on a finite interval for abstract singular equations

Cites Work

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• Criterion for the solvability of the Cauchy problem for an abstract Euler-Poisson-Darboux equation
• A note on fractional derivatives of semigroups and cosine functions
• Second-order linear differential equations in a Banach space and splitting operators
• Linear differential operators and operator matrices of the second order
• On the relationship between the integrated cosine function and the operator Bessel function
• Abstract Cauchy problem for the Bessel-Struve equation
• Spectral theory of linear relations on real Banach spaces
• Ordinary differential equations in linear topological space. II
• On the Equation of Euler–Poisson–Darboux

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