Strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with integrals

• Autorzy: Brandys J.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with integrals. For that systems we give strong maximum principles in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain.

Słowa kluczowe

EN

inequalities; integrals; parabolic differential functional

PL

nierówności; całki; paraboliczne funkcjonały różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 3
• Strony: 571--581
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Brandys J.

• Cracow University of Technology Independend Division of Descriptive Geometry and Engineering Graphics Warszawska 24, 31-155 Cracow, Poland

Bibliografia

• [1] L. Byszewski, Strong maximum principle for implicit non-linear parabolic functional-differential inequalities in arbitrary domains, Univ. Iagell. Acta Math. 24 (1984), 327-339.
• [2] L. Byszewski, Strong maximum and minimum principles for parabolic functional-differential problems with non-local inequalities [uj(t0, x)−Kj] +Pihi(x)[uj(Ti, x)−Kj]≤(≥)0, Ann. Polon. Math. 52 (1990), 195-204.
• [3] L. Byszewski, Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals, J. Appl. Math. Stochastic Anal. 3.5 (1990), 65-80.
• [4] J. Brandys, Strong maximum principles for infinite systems of parabolic differential-functional inequalities with initial constant estimates, Ann. Soc. Math. Polon., Comm. Math. 47.2 (2007), 141-148.
• [5] D. Jaruszewska-Walczak, Comparison theorems for infinite systems of parabolic functional-differential equations, Ann. Polon. Math. 77.3 (2001), 261-269.
• [6] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Acad. Publ., Dordrecht 1999.
• [7] Z. Kamont, Infinite systems of hyperbolic functional differential inequalities, Nonlinear Anal. 51 (2002), 1429-1445.
• [8] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93(1984), 109-131.
• [9] J. Szarski, Strong maximum principle for non-linear parabolic differential-functional inequalities, Ann. Polon. Math. 29 (1974), 207-214.
• [10] J. Szarski, Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domains, Ann. Polon. Math. 31 (1975), 197-203.
• [11] J. Szarski, Infinite systems of parabolic differential-functional inequalities, Bull. Acad. Polon. Sci., Sér. Sci. Math. 28.9-10 (1980), 477-481.
• [12] P. N. Vabishchevich, Non-local parabolic problems and the inverse heat-conduction problem (in Russian), Diff. Uravn. 17 (1981), 1193-1199.