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Strong maximum principles for implicit parabolic functional-differential problems together with nonstandard inequalities with sums

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Abstrakty
EN
The aim of the paper is to give strong maximum principles for implicit parabolic functional - differential problems together with nonstandard inequalities with sums in relatively arbitrary (n + 1)-dimensional time-space sets more general than the cylindrical domain. The results obtained can be applied in the theory of diffusion and in the theory of heat conduction.
Wydawca
Rocznik
Strony
857--866
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
  • Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Cracow, Poland
Bibliografia
  • [1] P. Besala, An extension of the strong maximum principle for parabolic equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 19 (1971), 1003-1006.
  • [2] J. Brandys, L. Byszewski, Uniqueness of solutions to inverse parabolic problems, Comment. Math. 42.1 (2002), 17-30.
  • [3] L. Byszewski, Strong maximum principle for implicit nonlinear parabolic functional differential inequalities in arbitrary domains, Univ. Iagell. Acta Math. 24 (1984), 327-339.
  • [4] L. Byszewski, Strong maximum and minimum principles for parabolic functional-differential problems with non-local inequalities […], Ann. Polon. Math. 52 (1990), 195-204.
  • [5] L. Byszewski, Existence and uniqueness of classical solutions to semilinear Darboux problems together with nonstandard conditions with integrals, Comment. Math. 43.2 (2003), 169-183.
  • [6] L. Byszewski, Strong maximum principles for implicit parabolic functional-differential problems together with initial inequalities, Ann. Acad. Ped. Cracov., Studia Math. 23.IV (2004), 9-16.
  • [7] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131.
  • [8] R. Redheffer, W. Walter, Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Punktionalen, Math. Ann. 226 (1977), 155-170.
  • [9] J. Szarski, Differential Inequalities, PWN, Warszawa 1967.
  • [10] J. Szarski, Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domains, Ann. Polon. Math. 29 (1974), 207-217.
  • [11] J. Szarski, Inifinite systems for parabolic differential-functional inequalities, Bull. Acad. Polon. Sci. Ser. Sci. Math. 28 (1980), 471-481.
  • [12] W. Walter, Differential and Integral Inequalities, Springer-Verlag, Berlin, Heidelberg, New York 1970.
  • [13] N. Yoshida, Maximum principles for implicit parabolic equations, Proc. Japan Acad. 49 (1973), 785-788.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0011-0009
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