Explicit solution of a class of higher-order abstract Cauchy problems

DOI10.1016/0022-0396(70)90030-6zbMath0208.38603OpenAlexW2017076450MaRDI QIDQ2543727

Reuben Hersh

Publication date: 1970

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

Full work available at URL: https://doi.org/10.1016/0022-0396(70)90030-6

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items

Temporally inhomogeneous Timoshenko beam equations, Some Abstract Cauchy Problems in Exceptional Cases, Algebraic and differential operator equations, Integral representation and stabilization of the solution to the Cauchy problem for an equation with two noncommuting operators, Random evolutions are asymptotically gaussian, Unnamed Item, The Cauchy problem for a first order system of abstract operator equations, Probabilistic representations for the solution of higher order differential equations, Transmutations that introduce group operators, Theory of Random Evolutions with Applications to Partial Differential Equations, Some asymptotic properties of solutions of nonlinear abstract wave equations, On some hyperbolic equations with operator coefficients, Equipartition of energy for a class of second order equations, A uniqueness theorem for epd type equations in general spaces, The abstract Cauchy problem, Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces, Higher order abstract Cauchy problems, Large-time behavior of solutions of abstract wave equations, Hyperbolic equations with coefficients in an enveloping algebra, Integrated semigroups and their application to complete second order Cauchy problems, Semigroups of operators, cosine operator functions, and linear differential equations, Diffusion transforms, On the invariance principle of scattering theory

Cites Work

• Singular perturbations for the Cauchy problem and for boundary value problems
• Singularly perturbed differential equations in a Hilbert space
• Perturbation and approximation theory for higher-order abstract Cauchy problems
• On one-parameter groups of linear transformations. I
• An operational calculus for operators with spectrum in a strip
• Une généralisation du problème de Cauchy
• Related problems in partial differential equations
• RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
• DIRECT SOLUTION OF GENERAL ONE-DIMENSIONAL LINEAR PARABOLIC EQUATION VIA AN ABSTRACT PLANCHEREL FORMULA
• A Perturbation Series for Cauchy's Problem for Higher-Order Abstract Parabolic Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item