The method of integrated semigroups for Cauchy problems in Banach spaces

DOI10.1007/BF02674296zbMath0920.34054OpenAlexW2008812254MaRDI QIDQ1288089

Irina V. Melnikova

Publication date: 10 May 1999

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02674296

zbMATH Keywords

Cauchy problemcorrectnessnecessary and sufficient conditionsecond-order operator-differential equation

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Linear differential equations in abstract spaces (34G10)

Related Items (3)

Integrated semigroups and \(C\)-semigroups and their applications ⋮ Local k-convoluted c-semigroups and complete second order abstract Cauchy problems ⋮ Structural theorems for ultradistribution semigroups

Cites Work

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• Integrated semigroups
• Vector-valued Laplace transforms and Cauchy problems
• On complete second order linear differential equations in Banach spaces
• Integrated semigroups and their applications to the abstract Cauchy problem
• Singular perturbation and boundary layer for an abstract Cauchy problem
• Conditions for parabolicity of second order abstract differential equations
• Generation theorem of semigroup for multivalued linear operators
• Existence for implicit differential equations in Banach spaces
• Integrated semigroups and their application to complete second order Cauchy problems
• General theory of the ill-posed Cauchy problem

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