Periodicity and Stability for Linear and Quasi-Linear Parabolic Equations
Carl T. Kallina · SIAM Journal on Applied Mathematics · 1970
Previous article Next article Periodicity and Stability for Linear and Quasi-Linear Parabolic EquationsCarl KallinaCarl Kallinahttps://doi.org/10.1137/0118053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Paul Fife, Solutions of parabolic boundary problems existing for all time, Arch. Rational Mech. Anal., 16 (1964), 155–186 10.1007/BF00250642 MR0167727 (29:4999) 0173.38204 CrossrefISIGoogle Scholar[2] I. I. Šmulev, Periodic solutions of the first boundary-value problem for parabolic equations, Mat. Sb. (N.S.), 66 (108) (1965), 398–410, (In Russian.) MR0173097 (30:3312) Google Scholar[3] Mitsuhiko Kono, Remarks on periodic solutions of linear parabolic differential equations of the second order, Proc. Japan Acad., 42 (1966), 5–9 MR0211033 (35:1918) 0163.34103 CrossrefGoogle Scholar[4] Takasi Kusano, A remark on a periodic boundary problem of parabolic type, Proc. Japan Acad., 42 (1966), 10–12 MR0211034 (35:1919) 0166.37102 CrossrefGoogle Scholar[5] Takasi Kusano, Periodic solutions of the first boundary problem for quasilinear parabolic equations of second order, Funkcial. Ekvac, 9 (1966), 129–137 MR0209684 (35:581) 0154.36101 Google Scholar[6] Mitsuhiko Kono and , Takasi Kusano, A boundary value problem for nonlinear parabolic equations of the second order, Comment. Math. Univ. St. Paul., 14 (1966), 85–96 MR0200613 (34:504) 0163.34104 Google Scholar[7] S. J. Farlow, Periodic solutions of parabolic partial differential equations, Tech. Rep., 32, Oregon State University, Corvallis, Oregon, 1967 Google Scholar[8] O. A. Olei˘nik and , T. D. Ventcel, The first boundary problem and the Cauchy problem for quasi-linear equations of parabolic type, Mat. Sb. N.S., 41(83) (1957), 105–128, (In Russian.) MR0086247 (19,149g) Google Scholar[9] T. D. Ventcel, On the application of the method of finite differences to the solution of the first boundary problem for equations of parabolic type, Mat. Sb. N.S., 40(82) (1956), 101–122 MR0090882 (19,885c) Google Scholar[10] O. Oleinik and , S. Krushkov, Quasilinear second order parabolic equations with many independent variables, Russian Math. Surveys, 16 (1961), 105–146 10.1070/rm1961v016n05ABEH004114 0112.32604 CrossrefGoogle Scholar[11] George Seifert, Stability conditions for the existence of almost-periodic solutions of almost-periodic systems, J. Math. Anal. Appl., 10 (1965), 409–418 10.1016/0022-247X(65)90135-6 MR0173061 (30:3276) 0173.34902 CrossrefISIGoogle Scholar[12] A. Il'in, , A. Kalashnikov and , O. Oleinik, Linear equations of the second order of parabolic type, Russian Math. Surveys, 17 (1962), 1–143 10.1070/rm1962v017n03ABEH004115 CrossrefGoogle Scholar[13] I. I. Šmulev, Almost periodic solutions of a parabolic equation, Sibirsk. Mat. Ž, 7 (1966), 685–698, (In Russian.) MR0200584 (34:475) 0174.42002 Google Scholar[14] C. Kallina, Masters Thesis, Periodic and almost periodic solutions of a class of quasilinear parabolic equations, Doctoral thesis, The Catholic University of America, Washington, D.C., 1967. Google Scholar[15] L. Amerio, Almost-periodic solutions of limit systems of non-linear almost-periodic differential equations, Ann. Mat. Pura Appl., 39 (1955), 97–119, (In Italian.) CrossrefGoogle Scholar[16] R. Narasimhan, On the asymptotic stability of solutions of parabolic differential equations, J. Rational Mech. Anal., 3 (1954), 303–313 MR0061260 (15,799c) 0055.32602 ISIGoogle Scholar[17] S. J. Farlow, An existence theorem for periodic solutions of a parabolic boundary value problem of the second kind, SIAM J. Appl. Math., 16 (1968), 1223–1226 10.1137/0116102 MR0239278 (39:635) 0172.14602 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails New oscillation theorems for a class of second-order damped nonlinear differential equationsUkrainian Mathematical Journal, Vol. 63, No. 9 | 18 March 2012 Cross Ref The heat equationPartial differential equations: time-periodic solutions | 1 Jan 1982 Cross Ref Full non-linear treatment of the global thermospheric wind system—I. Mathematical method and analysis of forcesJournal of Atmospheric and Terrestrial Physics, Vol. 37, No. 2 | 1 Feb 1975 Cross Ref Volume 18, Issue 3| 1970SIAM Journal on Applied Mathematics539-719 History Submitted:24 December 1968Published online:01 August 2006 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118053Article page range:pp. 601-613ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics