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Existence and uniqueness of solution are proved for elastodynamics of Reissner-Mindlin plate model. Higher regularity is proved under the assumptions of smoother data and certain compatibility conditions. A mass scaling is introduced. When the thickness approaches zero, the solution of the clamped Reissner-Mindlin plate is shown to approach the solution of a Kirchhoff-Love plate.
We study uniform finite-difference method for solving first-order singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis.
This work is concerned with a semilinear thermoelastic system, where the heat flux is given by Cattaneo's law instead of the usual Fourier's law. We will improve our earlier result by showing that the blowup can be obtained for solutions with relatively positive initial energy. Our technique of proof is based on a method used by Vitillaro with the necessary modifications imposed by the nature of our problem.
Scaling limits of continuous-time random walks are used in physics to model anomalous diffusion in which particles spread at a different rate than the classical Brownian motion. In this paper, we characterize the scaling limit of the average of multiple particles, independently moving as a continuous-time random walk. The limit is taken by increasing the number of particles and scaling from microscopic to macroscopic view. We show that the limit is independent of the order of these limiting procedures and can also be taken simultaneously in both procedures. Whereas the scaling limit of a single-particle movement has quite an obscure behavior, the multiple-particle analogue has much nicer properties.
An SI epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility, natural mortality, and disease-induced mortality rates depend on age and the force of infection corresponds to a special form of intercohort transmission called proportionate mixing. We determine the steady states and obtain explicitly computable threshold conditions, and then perform stability analysis.
A periodic time-dependent Lotka-Volterra-type predator-prey model with stage structure for the predator and time delays due to negative feedback and gestation is investigated. Sufficient conditions are derived, respectively, for the existence and global stability of positive periodic solutions to the proposed model.