PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 134 | 1 | 79-98
Tytuł artykułu

On coerciveness in Besov spaces for abstract parabolic equations of higher order

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We are concerned with a relation between parabolicity and coerciveness in Besov spaces for a higher order linear evolution equation in a Banach space. As proved in a preceding work, a higher order linear evolution equation enjoys coerciveness in Besov spaces under a certain parabolicity condition adopted and studied by several authors. We show that for a higher order linear evolution equation coerciveness in Besov spaces forces the parabolicity of the equation. We thus conclude that parabolicity and coerciveness in Besov spaces are equivalent.
Słowa kluczowe
Czasopismo
Rocznik
Tom
134
Numer
1
Strony
79-98
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-04-08
poprawiono
1998-06-10
Twórcy
  • Department of Applied Physics, Faculty of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan, yamamoto@ap.eng.osaka-u.ac.jp
Bibliografia
  • [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
  • [2] H. Brézis and L. E. Fraenkel, A function with prescribed initial derivatives in different Banach spaces, J. Funct. Anal. 29 (1978), 328-335.
  • [3] P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Springer, Berlin, 1967.
  • [4] G. Da Prato et P. Grisvard, Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl. 54 (1975), 305-387.
  • [5] G. Da Prato and E. Sinestrari, Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa 14 (1987), 285-344.
  • [6] G. Di Blasio, Linear parabolic evolution equations in $L^p$-spaces, Ann. Mat. 138 (1984), 55-104.
  • [7] Yu. A. Dubinskiĭ, On some differential-operator equations of arbitrary order, Math. USSR-Sb. 19 (1973), 1-21.
  • [8] A. Favini and E. Obrecht, Conditions for parabolicity of second order abstract differential equations, Differential Integral Equations 4 (1991), 1005-1022.
  • [9] A. Favini and H. Tanabe, On regularity of solutions to n-order differential equations of parabolic type in Banach spaces, Osaka J. Math. 31 (1994), 225-246.
  • [10] P. Grisvard, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl. 45 (1966), 207-290.
  • [11] P. Grisvard, Équations différentielles abstraites, Ann. Sci. École Norm. Sup. 2 (1969), 311-395.
  • [12] J. Lagnese, On equations of evolution and parabolic equations of higher order in t, J. Math. Anal. Appl. 32 (1970), 15-37.
  • [13] T. Muramatu, On Besov spaces of functions defined in general regions, Publ. R.I.M.S. Kyoto Univ. 6 (1970),//1971 515-543.
  • [14] T. Muramatu, On Besov spaces and Sobolev spaces of generalized functions defined on a general region, ibid. 9 (1974), 325-396.
  • [15] T. Muramatu, Besov spaces and analytic semigroups of linear operators, J. Math. Soc. Japan 42 (1990), 133-146.
  • [16] E. Obrecht, Sul problema di Cauchy per le equazioni paraboliche astratte di ordine n, Rend. Sem. Mat. Univ. Padova 53 (1975), 231-256.
  • [17] E. Obrecht, Evolution operators for higher order abstract parabolic equations, Czechoslovak Math. J. 36 (111) (1986), 210-222.
  • [18] E. Obrecht, The Cauchy problem for time-dependent abstract parabolic equations of higher order, J. Math. Anal. Appl. 125 (1987), 508-530.
  • [19] E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl. 107 (1985), 16-66.
  • [20] P. E. Sobolevskiĭ, Coerciveness inequalities for abstract parabolic equations, Soviet Math. Dokl. 5 (1964), 894-897.
  • [21] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
  • [22] H. Tanabe, Volterra integro-differential equations of parabolic type of higher order in t, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), 111-125.
  • [23] H. Tanabe, On fundamental solutions of linear parabolic equations of higher order in time and associated Volterra equations, J. Differential Equations 73 (1988), 288-308.
  • [24] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
  • [25] Y. Yamamoto, Remarks on coerciveness in Besov spaces for abstract parabolic equations, J. Math. Kyoto Univ. 34 (1994), 207-218.
  • [26] Y. Yamamoto, Solutions in Besov spaces of a class of abstract parabolic equations of higher order in time, ibid. 38 (1998), 201-227.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv134i1p79bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.