相关论文: Cloaking via mapping for the heat equation

Due to the highly degeneracy and singularities of the entropy equation, the physical entropy for viscous and heat conductive polytropic gases behave singularly in the presence of vacuum and it is thus a challenge to study its dynamics. It…

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…

This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we…

Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem…

In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first…

We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation…

Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and…

We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak $H^1$-convergence is given, which reduces to the original equation when the…

We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…

We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled…

Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…

We consider approximate cloaking from a regularization viewpoint introduced in [13] for EIT and further investigated in [12] [17] for the Helmholtz equation. The cloaking schemes in [12] and [17] are shown to be (optimally) within…

Thermodynamics and transport properties of a dissipative particle in a tight-binding model are studied through specific heat and optical conductivity. A weak coupling theory is constituted to study the crossover behavior between the…

We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup…

We approximate the heat kernel $h(x,y,t)$ on a compact connected Riemannian manifold $M$ without boundary uniformly in $(x,y,t)\in M\times M\times [a,b]$, $a>0$, by $n$-fold integrals over $M^n$ of the densities of Brownian bridges.…

We demonstrate that quantum mechanics entails a fundamental lower bound on the thermalization time $\tau$ of any system. At finite temperature, we show that $\tau$ is bounded by half the Planckian dissipation time, $\tau \geq \tau_{\rm…

We develop a method to study the structure of the common part of the boundaries of disjoint and possibly non-complementary time-varying domains in $\mathbb{R}^{n+1}$, $n \geq 2$, at the points of mutual absolute continuity of their…

We show that liquids and certain holographic models are strikingly similar in terms of several detailed and specific properties related to their energy spectra. We consider two different holographic models and ascertain their similarity…

In recent years a remarkable progress was made in the construction of spatial cloaks using the methods of transformation optics and metamaterials. The temporal cloaking, i.e. the cloaking of an event in spacetime, was also widely studied by…

In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding…