Related papers: Approximate analytical solution for transient heat…
The dispersion phenomenon of mass and heat transport in oscillatory flows has wide applications in environmental, physiological and microfluidic flows. The method of concentration moments is a powerful theoretical tool for analyzing…
In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
We consider fluid flow across a permeable interface within a deformable porous medium. We use mixture theory. The mixture's constituents are assumed to be incompressible in their pure form. We use Hamilton's principle to obtain the…
We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…
We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the…
We investigate the subtle effects of diffuse charge on interfacial kinetics by solving the governing equations for ion transport (Nernst-Planck) with realistic boundary conditions representing reaction kinetics (Butler-Volmer) and…
The relationship between the spatiotemporal distribution of oxygen transport and blood flow dynamics, accounting for the motion and deformation of individual red blood cells (RBCs), is of fundamental importance for understanding…
Global solutions to the compressible Euler equations with heat transport by convection in the whole space are shown to exist through perturbations of Dyson's isothermal affine solutions. This setting presents new difficulties because of the…
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
A coupled cohesive zone model based on an analogy between fracture and contact mechanics is proposed to investigate debonding phenomena at imperfect interfaces due to thermomechanical loading and thermal fields in bodies with cohesive…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
We present a technique, {\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…