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We present a simple analytic gravitational solution which describes the holographic dual of a 2+1-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in…
The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective…
We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state…
The flexible profile approach proposed earlier to create CTM (compact or reduced order thermal models) is extended to cover the area of conjugate heat transfer. The flexible profile approach is a methodology that allows building a highly…
We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…
In this short paper, periodic homogenization of a steady heat flow in two-component media with highly adhesive contact is performed via the two-scale convergence technique. Our micro-model is based on mass conservation for the heat flow in…
We consider an inverse boundary value problem for the heat equation $\partial_t v = {\rm div}_x\,(\gamma\nabla_x v)$ in $(0,T)\times\Omega$, where $\Omega$ is a bounded domain of $R^3$, the heat conductivity $\gamma(t,x)$ admits a surface…
We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of…
We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has…
An explicit solution of a similarity type is obtained for a one-phase Stefan problem in a semi-infinite material using Kummer functions. Motivated by [D.A. Tarzia, Relationship between Neumann solutions for two phase Lam\'e-Clapeyron-Stefan…
The fluid flow across an unbounded horizontal plate embedded with uniform mass diffusion is studied in this article together with the impacts of the chemical reaction and parabolic motion, while the temperature and concentration of the…
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…
A thermodynamic framework that predicts the thermal conductivity $\lambda$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in…
Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within…
The new generation of manufacturing technologies such as e.g. additive manufacturing and automated fiber placement has enabled the development of material systems with desired functional and mechanical properties via particular designs of…
We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…