The Existence of Periodic Solutions to Reaction-Diffusion Systems with Periodic Data

Abstract

Previous article Next article The Existence of Periodic Solutions to Reaction-Diffusion Systems with Periodic DataJ. J. Morgan and S. L. HollisJ. J. Morgan and S. L. Hollishttps://doi.org/10.1137/S0036141093257179PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe existence of time-periodic solutions is proven for a large class of reaction-diffusion systems in which Dirichlet boundary data, diffusivities, and reaction rates are periodic with common period.[1] Herbert Amann, Periodic solutions of semilinear parabolic equationsNonlinear analysis (collection of papers in honor of Erich H. Rothe), Academic Press, New York, 1978, 1–29 80a:35009 0464.35050 CrossrefGoogle Scholar[2] D. Bange, An existence theorem for periodic solutions of a nonlinear parabolic boundary value problem, J. 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Differential Equations, 19 (1975), 242–257 10.1016/0022-0396(75)90004-2 57:10184 0281.35005 CrossrefISIGoogle ScholarKeywordsperiodic solutionsreaction-diffusion systems Previous article Next article FiguresRelatedReferencesCited ByDetails New insights into pharmacologic inhibition of pyroptotic cell death by necrosulfonamide: A PDE modelNonlinear Analysis: Real World Applications, Vol. 56 | 1 Dec 2020 Cross Ref Global existence for semilinear reaction–diffusion systems on evolving domainsJournal of Mathematical Biology, Vol. 64, No. 1-2 | 4 February 2011 Cross Ref Mathematical Analysis and Pattern Formation for a Partial Immune System Modeling the Spread of an Epidemic DiseaseActa Applicandae Mathematicae, Vol. 115, No. 1 | 20 May 2010 Cross Ref A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic EquationsAbstract and Applied Analysis, Vol. 2011 | 1 Jan 2011 Cross Ref Asymptotic behavior of solutions of a periodic diffusion systemJournal of Mathematical Analysis and Applications, Vol. 370, No. 2 | 1 Oct 2010 Cross Ref On the Time Periodic Free Boundary Associated to Some Nonlinear Parabolic EquationsBoundary Value Problems, Vol. 2010, No. 1 | 1 Jan 2010 Cross Ref Proof of existence of global solutions for m -component reaction–diffusion systems with mixed boundary conditions via the Lyapunov functional methodJournal of Physics A: Mathematical and Theoretical, Vol. 40, No. 41 | 25 September 2007 Cross Ref Controllability Methods for the Computation of Time-Periodic Solutions; Application to ScatteringJournal of Computational Physics, Vol. 147, No. 2 | 1 Dec 1998 Cross Ref Asymptotic periodicity and permanence in a competition-diffusion system with discrete delaysApplied Mathematics and Computation, Vol. 89, No. 1-3 | 1 Jan 1998 Cross Ref Periodic solution and oscillation in a competition model with diffusion and distributed delay effectsNonlinear Analysis: Theory, Methods & Applications, Vol. 27, No. 6 | 1 Sep 1996 Cross Ref Asymptotic periodicity in diffusive logistic equations with discrete delaysNonlinear Analysis: Theory, Methods & Applications, Vol. 26, No. 2 | 1 Jan 1996 Cross Ref Volume 26, Issue 5| 1995SIAM Journal on Mathematical Analysis1089-1402 History Submitted:25 September 1993Accepted:17 January 1994Published online:17 February 2012 InformationCopyright © 1995 Society for Industrial and Applied MathematicsKeywordsperiodic solutionsreaction-diffusion systemsMSC codes3581035K4535K57PDF Download Article & Publication DataArticle DOI:10.1137/S0036141093257179Article page range:pp. 1225-1232ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics