Semilinear functional differential equations in Banach space

ABSTRACT. We consider a diffusive variant of the basic age-structured SEIR epidemic model with time dependent source terms. The source term for susceptibles appears as a forcing term and the source term for the infectives appears as a boundary condition at the age boundary a -0. We produce the a priori estimates requisite for guaranteeing the existence of time periodic solutions in response to time periodicity in the forcing functions. Properties of the periodic solutions are also investigated.

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“…We set Finally, we know that the operator V(t, s) is a compact mapping of C(fi) to itself, cf. [1]. We have the following compactness result.…”

Section: B) = D2andvfa T) -X(t)vfa T) + F 3 Fa T U) (219c) Atmentioning

confidence: 87%

Periodicity in diffusive age-structured SEIR models

Fitzgibbon¹,

Morgan²,

Parrott³

1998

Methods and Applications of Analysis

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“…The books of Pazy [4], Krien [7] and Fitzgibbon [8] contained therein, give a good account of important results. We mention here only some notation and properties essential to our purpose, In particular, we assume that T(t+s)=T(t)T(s), t,s 0  T(0)=I ,(T(0) is the identity operator on X).…”

Section: Definitionmentioning

confidence: 99%

Existence and Uniqueness for a Class of Semilinear Initial Value Control Problems in Suitable Banach Spaces

Salah¹,

Yousif²,

Ahmood³

2008

JNUS

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The local existence and uniqueness of S-classical solution (semi-classical solution) for a class of semilinear initial value control problems in suitable Banach spaces have been discussed and proved. The theoretical results are depending on the theory of analytic semigroup and Banach contraction principle.Keywords: S-classical solution (semi-classical solution), control problem in infinite dimensional spaces, fixed point theorem and analytic semigroup theory.

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“…To 'illustrate only one feature, let us remind (see [96] [9], [28], [3.l], [32], [34], [39], [41], [43], [46], [75], Ie3], Ie4], Ie7], [99], ttO+1, [157], It58], [173], [209] [38]) .…”

Section: |67])mentioning

confidence: 99%

“…Nevertheless, it would be interesting to see whether S can be chosen conveniently for the system (37) or (49), such that the theorem of K. Sawano [84], [210], lzILf, [162], [163] [35], [36] (75) reduces to the corresponding problem for fz = f More prec'ise'ly, the Fredholm alternative is simultaneously true for (75) and Tz = f (and their adiojnt equations). 0f course, particularizing conveniently r(t,s) and p(t,s) in (75), one obtains equations with unbounded de1ay.-In particu]ar, (78) (83). An interesting result regards the orbital stability of a periodic solution p(t) of the "autonomous" system (85) i(t) -r(z(t),(k*z) (111 , where * indicates the convolut'ion product.…”

Section: |67])mentioning

confidence: 99%