Aronszajn's theorem for a parabolic partial differential equation

DOI10.1016/0362-546X(85)90029-XzbMath0583.35053OpenAlexW2084558114WikidataQ115363585 ScholiaQ115363585MaRDI QIDQ3708439

Michael E. Ballotti

Publication date: 1985

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(85)90029-x

zbMATH Keywords

evolution equationmild solutionnontrivial solutionssolution funnel\(C_ 0\)-semigroupcompact absolute retracts

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Nonlinear parabolic equations (35K55) Equations involving nonlinear operators (general) (47J05) Nonlinear differential equations in abstract spaces (34G20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items

Kneser's property for a parabolic partial differential equation, Evolution problems with nonlinear nonlocal boundary conditions, The set of solutions for certain semilinear heat equations, The Hukuhara-Kneser property for a nonlinear integral equation, Properties of the solution set of nonlinear evolution inclusions, On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Aronszajn's theorem for some nonlinear Dirichlet problems with unbounded nonlinearities, Structure of the set of solutions of an initial-boundary value problem for a parabolic partial differential equation in an unbounded domain, A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set, Periodic problems and problems with discontinuities for nonlinear parabolic equations, A continuum of solutions in a Fréchet space of a nonlinear functional integral equation in N variables

Cites Work

• A class of semi-linear equations of evolution
• Funnel sections
• The shape of a cross-section of the solution funnel of an ordinary differential equation
• Le correspondant topologique de l'unicité dans la théorie des équations différentielles
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