We consider a class of inverse source problems for the parabolic approximation to the Maxwell equations using a Bayesian approach.

Consider the semilinear parabolic equation −ut(x, t) + uxx + q(u) = f(x, t), with the initial condition u(x, 0) = u0(x), Dirichlet boundary conditions u(0, t) = φ0(t), u(1, t) = φ1(t) and a sufficiently regular source term q(·), which is assumed to be known a priori on the range of u0(x). We investigate the inverse problem of determining the function q(·) outside this range from measurements of...

in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

in this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. then a common general forward modeling for them is given and the corresponding inversion problem is presented. then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a baye...

This paper is intended to provide a stochastic approach involving the combined use of the Feynman-Kac formula and Monte Carlo method as a solution algorithm for estimating the timedependent effective diffusivity in a one-dimensional parabolic inverse problem. The inverse problem is purposed to design a mathematical model for the gas-diffusion process within the alveolar region of the human's lu...