caa a22 4500 378878522 CHVBK 20180305123426.0 cr unu---uuuuu 161128e200309 xx s 000 0 eng 10.1515/GMJ.2003.495 doi (NATIONALLICENCE)gruyter-10.1515/GMJ.2003.495 Domoshnitsky Alexander The College of Judea and Samaria, Ariel 44837, Israel. E-mail: adom@research.yosh.ac.il About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations [Elektronische Daten] [Alexander Domoshnitsky] In this paper, oscillation and asymptotic properties of solutions of the Dirichlet boundary value problem for hyperbolic and parabolic equations are considered. We demonstrate that introducing an arbitrary constant delay essentially changes the above properties. For instance, the delay equation does not inherit the classical properties of the Dirichlet boundary value problem for the heat equation: the maximum principle is not valid, unbounded solutions appear while all solutions of the classical Dirichlet problem tend to zero at infinity, for "narrow enough zones” all solutions oscillate instead of being positive. We establish that the Dirichlet problem for the wave equation with delay can possess unbounded solutions. We estimate zones of positivity of solutions for hyperbolic equations. © Heldermann Verlag Delay partial differential equations nationallicence oscillation nationallicence zone of positivity nationallicence unboundedness of solutions nationallicence Georgian Mathematical Journal Walter de Gruyter GmbH & Co. KG 10/3(2003-09), 495-502 1072-947X 10:3<495 2003 10 GMJ https://doi.org/10.1515/GMJ.2003.495 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/GMJ.2003.495 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Domoshnitsky Alexander The College of Judea and Samaria, Ariel 44837, Israel. E-mail: adom@research.yosh.ac.il NATIONALLICENCE 773 0- Georgian Mathematical Journal Walter de Gruyter GmbH & Co. KG 10/3(2003-09), 495-502 1072-947X 10:3<495 2003 10 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter