Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach

Luis Gerardo Mármol; Carmen Judith Vanegas

doi:10.33434/cams.446386

EN

Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach

Abstract

In this paper we study certain systems of mixed-type functional differential equations, from the point of view of the $C_{0}$-semigroup theory. In general, this type of equations are not well-posed as initial value problems. But there are also cases where a unique differentiable solution exists. For these cases and in order to achieve our goal, we first rewrite the system as a classical Cauchy problem in a suitable Banach space. Second, we introduce the associated semigroup and its infinitesimal generator and prove important properties of these operators. As an application, we use the results to characterize the null controllability for those systems, where the control $u$ is constrained to lie in a non-empty compact convex subset $\Om{}$ of $\R^n$.

Keywords

Functional differential equations,Strongly continuous semigroups,Mixed-type difference-differential equations,Exact controllability

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Luis Gerardo Mármol ^*
Venezuela

Carmen Judith Vanegas ^* This is me
Venezuela

Publication Date

December 24, 2018

Submission Date

July 20, 2018

Acceptance Date

October 4, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

DOI

https://doi.org/10.33434/cams.446386

IZ

https://izlik.org/JA33NJ79DS

APA

Mármol, L. G., & Vanegas, C. J. (2018). Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach. Communications in Advanced Mathematical Sciences, 1(2), 113-125. https://doi.org/10.33434/cams.446386

AMA

1.Mármol LG, Vanegas CJ. Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach. Communications in Advanced Mathematical Sciences. 2018;1(2):113-125. doi:10.33434/cams.446386

Chicago

Mármol, Luis Gerardo, and Carmen Judith Vanegas. 2018. “Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach”. Communications in Advanced Mathematical Sciences 1 (2): 113-25. https://doi.org/10.33434/cams.446386.

EndNote

Mármol LG, Vanegas CJ (December 1, 2018) Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach. Communications in Advanced Mathematical Sciences 1 2 113–125.

IEEE

[1]L. G. Mármol and C. J. Vanegas, “Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach”, Communications in Advanced Mathematical Sciences, vol. 1, no. 2, pp. 113–125, Dec. 2018, doi: 10.33434/cams.446386.

ISNAD

Mármol, Luis Gerardo - Vanegas, Carmen Judith. “Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach”. Communications in Advanced Mathematical Sciences 1/2 (December 1, 2018): 113-125. https://doi.org/10.33434/cams.446386.

JAMA

1.Mármol LG, Vanegas CJ. Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach. Communications in Advanced Mathematical Sciences. 2018;1:113–125.

MLA

Mármol, Luis Gerardo, and Carmen Judith Vanegas. “Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach”. Communications in Advanced Mathematical Sciences, vol. 1, no. 2, Dec. 2018, pp. 113-25, doi:10.33434/cams.446386.

Vancouver

1.Luis Gerardo Mármol, Carmen Judith Vanegas. Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach. Communications in Advanced Mathematical Sciences. 2018 Dec. 1;1(2):113-25. doi:10.33434/cams.446386

Cited By

On the stability and behavior of solutions in mixed differential equations with delays and advances

Mathematical Methods in the Applied Sciences

https://doi.org/10.1002/mma.8049

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