On solutions to abstract Volterra integro-differential equations with iterated deviating arguments
- 9 Downloads
We study the existence and uniqueness of solutions for a non-autonomous Volterra integro-differential equation of parabolic type with iterated deviating arguments in an arbitrary Banach space. The existence of a solution is established in a Banach space with smooth source terms in a Banach space. While the existence and uniqueness of a solution are proved in a Hilbert space without smoothness conditions. The continuation of a solution is also discussed of the problem. As an application, we illustrate the theory by an example.
KeywordsAnalytic semigroup Parabolic equation Plancherel theorem Schauder fixed point theorem
Mathematics Subject Classification34G20 34K30 35K90
The author would like to acknowledge the financial support for travel Grant from AICTE, NE QIP to attend the International conference on Mathematical Analysis and Its applications, IIT Roorkee, 2016 .
- 19.Haloi, R. 2012. A Study of Some Abstract Parabolic Initial Value Problems with Deviating Arguments. Thesis (Ph.D.), 170. IIT Kanpur (India).Google Scholar
- 26.Nohel, J.A.. Nonlinear Volterra equations for heat flow in materials with memory, MRC Tech. Summary Rp. 2081, Mathematics Research center, University of Wisconsin, Madison.Google Scholar
- 27.Sobolevskiĭ, P.L. 1966. Equations of parabolic type in a Banach space. American Mathematical Society Translations 49 (2): 1–62.Google Scholar