相关论文: Identification of the Heat Transfer Coefficient Us…
Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has…
D.Freed has formulated and proved an index theorem on odd dimensional spin manifolds with boundary. The proof is based on analysis by Calderon and Seeley. In this note we are going to give a proof of this theorem using the heat kernels…
The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is established by taking an…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…
In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…
The paper investigates non-stationary heat conduction in one-dimensional models with substrate potential. In order to establish universal characteristic properties of the process, we explore three different models --- Frenkel-Kontorova…
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…
The study of the paper mainly focusses on recovering the dissipative parameter in a cascade system coupling a bilaplacian operator to a heat equation from final time measured data via quasi-solution based optimization. The coefficient…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
We characterise the trace spaces arising from intersections of weighted, vector-valued Sobolev spaces, where the weights are powers of the distance to the boundary. These weighted function spaces are particularly suitable for treating…
Let $\Omega\subset\R^n$, $n\ge 3$, be a smooth bounded domain and consider a coupled system in $\Omega$ consisting of a conductivity equation $\nabla \cdot \gamma(x) \nabla u(t,x)=0$ and an anisotropic heat equation…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…
We consider an inverse shape problem coming from electrical impedance tomography with a generalized Robin transmission condition. We will derive an algorithm in order to detect whether two materials that should be in contact are separated…
Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain $D=\mathbb{R}^{n-1}\times\br^{+}$ for which the internal energy supply depends on an average in the…
We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, starting with the standard bidomain mathematical model related…