相关论文: An inverse problem for the heat equation

Marine heat flow data, obtained with a Lister-type probe, consists of two temperature decay curves, frictional and heat pulse decay. Both follow the same physical model of a cooling cylinder. The mathematical model describing the decays is…

In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…

The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the…

Transport properties in gases are significantly affected by temperature. In previous works it has been shown that when the thermal agitation in a gas is high enough, such that relativistic effects become relevant, heat dissipation is driven…

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(-\beta,\beta,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely.

In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…

The concept of "thermal inductance" expands the options of thermal circuit design. However, the inductive component is the only missing components in thermal circuits, unlike their electromagnetic counterparts. Herein, we report an…

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…

In this work, we consider a FDE (fractional diffusion equation) $${}^C D_t^\alpha u(x,t)-a(t)\mathcal{L} u(x,t)=F(x,t)$$ with a time-dependent diffusion coefficient $a(t)$. For the direct problem, given an $a(t),$ we establish the…

The full MHD problem of the flow and heat transfer due to a linearly stretching sheet in the presence of a transverse magnetic field is put in a self-similar form. Traditionally ignored physical processes such as induced magnetic field,…

A nearly universal feature of the specific heat curves C(T,U) vs. T for different U of a general class of Hubbard models is observed. That is, the value C_+ of the specific heat curves at their high-temperature crossing point T_+ is almost…

A complete family of solutions for the one-dimensional reaction-diffusion equation \[ u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t) \] with a coefficient $q$ depending on $x$ is constructed. The solutions represent the images of the heat polynomials…

We report measurements of the temperature fluctuations in a horizontal layer of a pure fluid confined between parallel plates and heated from below. Consistent with earlier work we found that the structure factor $S_T(q)$ (the square of the…

A complex integral formula provides an explicit solution of the initial value problem for the nonlinear scala 1D equation $u_t+[f(u)]_x = 0$, for any flux $f(u)$ and initial condition $u_0(x)$ that are analytic. This formula is valid at…

We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity…

We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressions $$ \mathfrak t_q:=\frac{1}{i}[I&0 0&-I]\frac{d}{dx}+[0&q q^*&0] $$ and some separated boundary conditions. Here $q$…

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…

This paper studies deformations of the well-known $\Xi(s)=\Xi(1-s)$ equation for the Riemann $\Xi$ function satisfied by $\Xi_\rho(s):=\int_{0}^\infty\frac{{\d}t}{t}{t^{\frac{s}{2}}}\Psi(t)e^{-\rho\ln^2(t)}$ where…

We study a nonlinear evolutionary partial differential equation that can be viewed as a generalization of the heat equation where the temperature gradient is a~priori bounded but the heat flux provides merely \mbox{$L^1$-coercivity}.…

Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…