12,387 research outputs found
A magneto-viscoelasticity problem with a singular memory kernel
The existence of solutions to a one-dimensional problem arising in
magneto-viscoelasticity is here considered. Specifically, a non-linear system
of integro-differential equations is analyzed, it is obtained coupling an
integro-differential equation modeling the viscoelastic behaviour, in which the
kernel represents the relaxation function, with the non-linear partial
differential equations modeling the presence of a magnetic field. The case
under investigation generalizes a previous study since the relaxation function
is allowed to be unbounded at the origin, provided it belongs to ; the
magnetic model equation adopted, as in the previous results [21,22, 24, 25] is
the penalized Ginzburg-Landau magnetic evolution equation.Comment: original research articl
On asymptotic effects of boundary perturbations in exponentially shaped Josephson junctions
A parabolic integro differential operator L, suitable to describe many
phenomena in various physical fields, is considered. By means of equivalence
between L and the third order equation describing the evolution inside an
exponentially shaped Josephson junction (ESJJ), an asymptotic analysis for
(ESJJ) is achieved, explicitly evaluating, boundary contributions related to
the Dirichlet problem
Population persistence under advection-diffusion in river networks
An integro-differential equation on a tree graph is used to model the
evolution and spatial distribution of a population of organisms in a river
network. Individual organisms become mobile at a constant rate, and disperse
according to an advection-diffusion process with coefficients that are constant
on the edges of the graph. Appropriate boundary conditions are imposed at the
outlet and upstream nodes of the river network. The local rates of population
growth/decay and that by which the organisms become mobile, are assumed
constant in time and space. Imminent extinction of the population is understood
as the situation whereby the zero solution to the integro-differential equation
is stable. Lower and upper bounds for the eigenvalues of the dispersion
operator, and related Sturm-Liouville problems are found, and therefore
sufficient conditions for imminent extinction are given in terms of the
physical variables of the problem
A mixed type identification problem related to a phase-field model with memory
In this paper we consider an integro-differential system consisting of a parabolic and a hyperbolic equation related to phase transition models. The first equation is integro-differential and of hyperbolic type. It describes the evolution of the temperature and also accounts for memory effects through a memory kernel k via the Gurtin-Pipkin heat flux law. The latter equation, governing the evolution of the order parameter, is semilinear, parabolic and of the fourth order (in space). We prove a local in time existence result and a global uniqueness result for the identification problem consisting in recovering the memory kernel k appearing in the first equation
A numerical method for the expected penalty–reward function in a Markov-modulated jump–diffusion process.
A generalization of the Cramér–Lundberg risk model perturbed by a diffusion is proposed. Aggregate claims of an insurer follow a compound Poisson process and premiums are collected at a constant rate with additional random fluctuation. The insurer is allowed to invest the surplus into a risky asset with volatility dependent on the level of the investment, which permits the incorporation of rational investment strategies as proposed by Berk and Green (2004). The return on investment is modulated by a Markov process which generalizes previously studied settings for the evolution of the interest rate in time. The Gerber–Shiu expected penalty–reward function is studied in this context, including ruin probabilities (a first-passage problem) as a special case. The second order integro-differential system of equations that characterizes the function of interest is obtained. As a closed-form solution does not exist, a numerical procedure based on the Chebyshev polynomial approximation through a collocation method is proposed. Finally, some examples illustrating the procedure are presentedExpected penalty–reward function; Markov-modulated process; Jump–diffusion process; Volterra integro-differential system of equations;
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