Global solutions for a new class of abstract neutral differential equations

Hernández, Eduardo; O’Regan, Donal

doi:10.1090/S0002-9939-2015-12508-7

Global solutions for a new class of abstract neutral differential equations
HTML articles powered by AMS MathViewer

by Eduardo Hernández and Donal O’Regan PDF

Proc. Amer. Math. Soc. 143 (2015), 3561-3571 Request permission

Abstract:

We study the existence of global solutions for a class of abstract neutral differential equations recently introduced in the literature. An application involving a partial neutral differential equation is presented.

References

Mostafa Adimy and Khalil Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain, J. Differential Equations 147 (1998), no. 2, 285–332. MR 1633941, DOI 10.1006/jdeq.1998.3446
Piermarco Cannarsa and Daniela Sforza, Global solutions of abstract semilinear parabolic equations with memory terms, NoDEA Nonlinear Differential Equations Appl. 10 (2003), no. 4, 399–430. MR 2016932, DOI 10.1007/s00030-003-1004-2
Richard Datko, Linear autonomous neutral differential equations in a Banach space, J. Differential Equations 25 (1977), no. 2, 258–274. MR 447743, DOI 10.1016/0022-0396(77)90204-2
Morton E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31 (1968), no. 2, 113–126. MR 1553521, DOI 10.1007/BF00281373
Said Hadd, Singular functional differential equations of neutral type in Banach spaces, J. Funct. Anal. 254 (2008), no. 8, 2069–2091. MR 2402084, DOI 10.1016/j.jfa.2008.01.011
Jack K. Hale, Partial neutral functional-differential equations, Rev. Roumaine Math. Pures Appl. 39 (1994), no. 4, 339–344. MR 1317773
Eduardo Hernández and Donal O’Regan, Existence of solutions for abstract non-autonomous neutral differential equations, Canad. Math. Bull. 55 (2012), no. 4, 736–751. MR 2994678, DOI 10.4153/CMB-2011-111-1
Eduardo Hernández and Donal O’Regan, $C^\alpha$-Hölder classical solutions for non-autonomous neutral differential equations, Discrete Contin. Dyn. Syst. 29 (2011), no. 1, 241–260. MR 2725289, DOI 10.3934/dcds.2011.29.241
José Paulo C. Dos Santos, Hernán Henríquez, and Eduardo Hernández, Existence results for neutral integro-differential equations with unbounded delay, J. Integral Equations Appl. 23 (2011), no. 2, 289–330. MR 2813436, DOI 10.1216/JIE-2011-23-2-289
Eduardo Hernández and Donal O’Regan, Existence results for abstract neutral functional differential equations, Proc. Amer. Math. Soc. 137 (2009), no. 10, 3309–3318. MR 2515400, DOI 10.1090/S0002-9939-09-09934-1
Eduardo Hernández and Hernán R. Henríquez, Existence results for partial neutral functional-differential equations with unbounded delay, J. Math. Anal. Appl. 221 (1998), no. 2, 452–475. MR 1621730, DOI 10.1006/jmaa.1997.5875
Eduardo Hernández, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292 (2004), no. 1, 194–210. MR 2050224, DOI 10.1016/j.jmaa.2003.11.052
Eduardo Hernández and Donal O’Regan, On a new class of abstract neutral differential equations, J. Funct. Anal. 261 (2011), no. 12, 3457–3481. MR 2838031, DOI 10.1016/j.jfa.2011.08.008
Yoshiyuki Hino, Satoru Murakami, and Toshiki Naito, Functional-differential equations with infinite delay, Lecture Notes in Mathematics, vol. 1473, Springer-Verlag, Berlin, 1991. MR 1122588, DOI 10.1007/BFb0084432
Alessandra Lunardi, Analytic semigroups and optimal regularity in parabolic problems, Modern Birkhäuser Classics, Birkhäuser/Springer Basel AG, Basel, 1995. [2013 reprint of the 1995 original] [MR1329547]. MR 3012216
Alessandra Lunardi, On the linear heat equation with fading memory, SIAM J. Math. Anal. 21 (1990), no. 5, 1213–1224. MR 1062400, DOI 10.1137/0521066
Jace W. Nunziato, On heat conduction in materials with memory, Quart. Appl. Math. 29 (1971), 187–204. MR 295683, DOI 10.1090/S0033-569X-1971-0295683-6
Jianhong Wu, Theory and applications of partial functional-differential equations, Applied Mathematical Sciences, vol. 119, Springer-Verlag, New York, 1996. MR 1415838, DOI 10.1007/978-1-4612-4050-1
S. Zaidman, Almost-periodic functions in abstract spaces, Research Notes in Mathematics, vol. 126, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 790316