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We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations ℰ ε ε , x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize theΓ-limit as ε → 0 of ℰε, and show that in general the Γ-limits of ℰεand x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of theΓ-limit of x10ff65;...
New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
In this paper, with the assumptions that an infectious disease has a fixed
latent period in a population and the latent individuals of the population may
disperse, we reformulate an SIR model for the population living in two patches
(cities, towns, or countries etc.), which is a generalization of the classic
Kermack-McKendrick SIR model. The model is given by a system of delay
differential equations with a fixed delay accounting for the latency and
non-local terms caused by the mobility of the...
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.
We describe the global dynamics of a disease transmission model between two regions which are connected via bidirectional or unidirectional transportation, where infection occurs during the travel as well as within the regions. We define the regional reproduction numbers and the basic reproduction number by constructing a next generation matrix. If the two regions are connected via bidirectional transportation, the basic reproduction number characterizes the existence of equilibria as well as...
In this paper Zadunaisky's technique is used to estimate the global error propagated in the numerical solution of the system of retarded differential equations by Euler's method. Some numerical examples are given.
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