Nonlocal Cauchy problems for semilinear evolution equations

DOI10.1016/S0362-546X(01)00743-XzbMath1009.34052OpenAlexW2154745208MaRDI QIDQ1612563

R. Smith

Publication date: 25 August 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(01)00743-x

zbMATH Keywords

fractional powerssemilinear evolution equationnonlocal Cauchy problemregularized semigroupsconvolution integralequation

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20)

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Cites Work

• Fractional powers of closed operators and the semigroups generated by them
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
• Uniqueness of solutions of parabolic semilinear nonlocal-boundary problems
• The Cauchy problem for higher-order abstract differential equations
• Existence families, functional calculi and evolution equations
• Fractional powers of operators with polynomially bounded resolvent and the semigroups generated by them
• Fractional powers of operators of regularized type
• Existence and uniqueness of solutions to semilinear nonlocal parabolic equations
• Theorem about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a banach space
• The Cauchy Problem and a Generalization of the Hille-Yosida Theorem
• Semilinear integrodifferential equations with nonlocal cauchy problem
• Application of monotone iterative method to a system of parabolic semilinear functional-differential problems with nonlocal conditions
• Equivalent Norms for Sobolev Spaces
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