相关论文: An inverse problem for the heat equation

The authors study the problem $u_t=u_{xx},\ 0<x<1,\ t>0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t<t_{2k+1}$ and $\psi(t)=0$ for $t_{2k+1} <t<t_{2k+2},\ k=0,1,2,\ldots$ with $t_0=0$ and the sequence…

Thermal management is a key challenge, both globally and microscopically in integrated circuits and quantum technologies. The associated heat flow $I_Q$ has been understood since the advent of thermodynamics by a process of elimination,…

In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing the…

In this paper we consider an inverse problem for determining time - dependent heat conduction coefficient which vanishes at initial moment as a power $ t^{\beta}. $ The case of strong degeneration ($ \beta \ge1$) is studied. To prove the…

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special…

A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…

This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…

What happens when one prescribes a heat flux which is proportional to the Neumann data of a solution of the wave equation in the whole space on the surface of a heat conductive body? It is shown that there is a difference in the asymptotic…

Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…

In this article, we demonstrate the phenomenon of thermal transpiration in a bounded convex domain. We employ the stationary Boltzmann equation with a cutoff potential. For boundary condition, we partition the boundary into diffuse…

In this investigation, symmetry properties of the nonlinear heat conductivity equations of general form $u_t = [E(x, u)u_x]_x + H(x, u)$ are studied. The point symmetry analysis of these equations is considered as well as an equivalence…

We consider a fractional diffusion equations of order $\alpha\in(0,1)$ whose source term is singular in time: $(\partial_t^\alpha+A)u(x,t)=\mu(t)f(x)$, $(x,t)\in\Omega\times(0,T)$, where $\mu$ belongs to a Sobolev space of negative order.…

This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…

The extraction problem of information about the location and shape of the cavity from a single set of the temperature and heat flux on the boundary of the conductor and finite time interval is a typical and important inverse problem. Its…

In this paper, we investigate a nonlinear inverse problem aimed at recovering a coefficient $a(t, x)$, dependent on both time and a subset of spatial variables, in a diffusion equation \( u_t - \Delta_x u - u_{yy} +a(t, x) u = f(t,x,y) \),…

In this paper we will study a stiff problem in two-dimensional space and especially its probabilistic counterpart. Roughly speaking, the heat equation with a parameter $\varepsilon>0$ is under consideration: \[ \partial_t…

In this paper, we revisit the claim that many partition functions are invariant under reflecting temperatures to negative values (T-reflection). The goal of this paper is to demarcate which partition functions should be invariant under…

We consider the scalar semilinear heat equation $u_t-\Delta u=f(u)$, where $f\colon[0,\infty)\to[0,\infty)$ is continuous and non-decreasing but need not be convex. We completely characterise those functions $f$ for which the equation has a…

We demonstrate that when a quantum dot is embedded between the two reservoirs described by different statistical distribution functions, the reverse flow and amplification of heat can be realized by regulating the energy levels of the…

State functions play important roles in thermodynamics. Different from the process function, such as the exchanged heat $\delta Q$ and the applied work $\delta W$, the change of the state function can be expressed as an exact differential.…