相关论文: Modelling silicosis: existence, uniqueness and bas…

Inspired by the paper Greenhalgh et al. [5] we investigate a class of two dimensional stochastic differential equations related to susceptible-infected-susceptible epidemic models with demographic stochasticity. While preserving the key…

In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity, temperature, and specific humidity. The main difficulty…

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…

Recently, we give the robust $\sim2\,\sigma$ evidences of dynamical dark matter and beyond $2\,\sigma$ signals of the coexistence of dynamical dark matter and dynamical dark energy using current cosmological observations [1]. Here we…

Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…

In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011), 876-902]. We…

The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…

We give a proof for the uniqueness of dissipative solution for the Camassa-Holm equation with some peakon-antipeakon initial data following Dafermos' earlier resut in [5] on the Hunter-Saxton equation. Our result shows that two existing…

In this paper we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising in the mathematical modeling of disease transmission. The direct problem is given by an initial boundary…

In the works of K.A. Pericak-Spector and S. Spector \cite{ps88, ps98} a class of self-similar solutions are constructed for the equations of radial isotropic elastodynamics that describe cavitating solutions. Cavitating solutions decrease…

Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that enlarge a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the…

We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…

As global living standards improve and medical technology advances, many infectious diseases have been effectively controlled. However, certain diseases, such as the recent COVID-19 pandemic, continue to pose significant threats to public…

The reaction-diffusion system of Fitzhugh Nagumo is considered. The initial- boundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several…

This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique existence theorem of the solution for initial value problems.…

This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…

We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…

In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider the cause of this…

One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face…

We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…