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

• Autorzy: Byszewski, L.
• Języki publikacji: EN

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.

Słowa kluczowe

PL

funkcje paraboliczne; nierówności; systemy nieliniowe

EN

parabolic functions; inequalities; strong maximum principles; implicit nonlinear systems

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 857--866
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Byszewski, L.

• 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.