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Strong maximum principles for infinite implicit systems with nonlocal inequalities

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Abstrakty
EN
The aim of the paper is to give strong maximum principles for infinite implicit systems of parabolic differential-functional inequalities with nonlocal inequalities together with sums in relatively arbitrary (n +1) − dimensional time - space sets more general than the cylindrical domain.
Rocznik
Strony
263--268
Opis fizyczny
Bibliogr. 22 poz., wzory
Twórcy
autor
  • Cracow University of Technology, Institute of Mathematics, Warszawska 24, 31-155 Cracow, Poland
Bibliografia
  • [1] P. Besala, An extension of the strong maximum principle for parabolic equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 1003 - 1006.
  • [2] J. Brandys, Strong maximum principles for infinite systems of parabolic differential-functional inequalities with initial constant estimates, Commentationes Mathematicae 47.2 (2007), 141-148.
  • [3] J. Brandys, Strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities[...] Fasciculi Mathematici 39 (2008), 17-26.
  • [4] S. Brzychczy, On the existence of solutions of nonlinear infinite systems of parabolic differential-functional equations, Univ. Iagel. Acta Math. 40 (2002), 31-38.
  • [5] [5] S. Brzychczy, Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations, Ann. Polon. Math. 77.1 (2001), 1-9.
  • [6] L. Byszewski, Strong maximum principles for implicit parabolic functional-differential problems together with initial inequalities, Annales Academiae Pedagogicae Cracoviensis, Studia Mathematica 23 (IV) (2004), 9-16.
  • [7] L. Byszewski, Strong maximum principles for implicit parabolic functional-differential problems together with nonstandard inequalities with sums, Demonstratio Mathematica 38.4 (2005), 857-866.
  • [8] L. Byszewski, Infinite implicit system of weak parabolic functional-differential inequalities and strong maximum principle for this infinite system, Czsopismo Techniczne, seria: Nauki Podstawowe (in press).
  • [9] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131.
  • [10] D. Jaruszewska-Walczak, Comparison theorems for infinite systems of parabolic functional-differential equations, Ann. Polon. Math. 77.3 (2001), 261-269.
  • [11] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Acad. Publ., Dordrecht 1999.
  • [12] Z. Kamont, Infinite systems of hyperbolic functional differential inequalities, Nonlinear Anal. 51 (2002), 1429-1445.
  • [13] V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, Vol. I, II, Academic Press, New York 1968.
  • [14] A. Pudełko, Existence of solutions for infinite systems for parabolic equations with functional dependence, Ann. Polon. Math. 86.2 (2005), 123-135.
  • [15] R . Redheffer, W. Walter, Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen, Math. Ann. 226 (1977), 155 -170.
  • [16] J. Szarski, Differential Inequalities, Polish Scientific Publishers, Warsaw 1967.
  • [17] J. Szarski, Strong maximum principle for non-linear parabolic differential - functional inequalities in arbitrary domains, Ann. Polon. Math. 29 (1974), 207 - 214.
  • [18] J. Szarski, Inifinite systems of parabolic differential - functional inequalities, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28.9-10 (1980), 471-481.
  • [19] W. Walter, Differential and Integral Inequalities, Springer Verlag, Berlin, Heidelberg, New York 1970.
  • [20] D. Wrzosek, Singular properties of solutions of Smoluchowski systems of equations (in Polish), Roczniki Polskiego Towarzystwa Matematycznego, Seria II: Wiadomości Matematyczne 35 (1999), 11-35.
  • [21] N. Yoshida, Maximum principles for implicit parabolic equations, Proc. Japan Acad. 49 (1973), 785-788.
  • [22] T. Zabawa, Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type, Opuscula Mathematica 26.1 (2006), 173-183.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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