This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish unknown coefficient. A finite difference scheme is constructed and a numerical approximation made. Examples experiments, such as man-made noise, provided show stability efficiency this method.

The aim of this paper is to propose an original numerical approach for parabolic problems whose governing equations are defined on unbounded domains. We are interested in studying the class of problems admitting invariance property to Lie group of scalings. Thanks to similarity analysis the parabolic problem can be transformed into an equivalent boundary value problem governed by an ordinary di...

reflection seismic data consist of primary reflections, coherent and incoherent noises. one of the objectives of seismic data processing is to enhance the quality of the real signals by attenuating different kinds of noises. multiples constitute one of the most troublesome forms of coherent noises in exploration seismology. multiple reflections often destructively interfere with the desired pri...

In oil production it is crucial to find out properties of the ground from various measurements of geophysical fields. In secondary oil recovery oil is extracted by pumping in water (through injecting wells) and creating pressure which pumps out oil through production wells. Water/oil pressure at wells is monitored providing with an information to determine two important characterictics of mediu...

The inverse problem of finding the coefficient γ in the equation u̇ = A(t)u + γ(t)u + f(t) from the extra data of the form φ(t) = 〈u(t), w〉 is studied. The problem is reduced to a Volterra equation of the second kind. Applications are given to parabolic equations with second order differential operators.

Abstract. An inverse problem for the identification of an unknown coefficient in a quasilinear parabolic partial differential equation is considered. We present an approach based on utilizing adjoint versions of the direct problem in order to derive equations explicitly relating changes in inputs (coefficients) to changes in outputs (measured data). Using these equations it is possible to show ...

We study the following “inverse first passage time” problem. Given a diffusion process Xt and a probability distribution q on [0,∞), does there exist a boundary b(t) such that q(t) = P[τ ≤ t], where τ is the first hitting time of Xt to the time dependent level b(t). A free boundary problem for a parabolic partial differential operator is associated with the inverse first passage time problem. W...

A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connecti...

We consider the statistical nonlinear inverse problem of recovering absorption term $f>0$ in heat equation $$ \partial_tu-\frac{1}{2}\Delta u+fu=0 \quad \text{on $\mathcal{O}\times(0,\textbf{T})$}\quad u = g $\partial\mathcal{O}\times(0,\textbf{T})$}\quad u(\cdot,0)=u_0 $\mathcal{O}$}, where $\mathcal{O}\in\mathbb{R}^d$ is a bounded domain, $\textbf{T}<\infty$ fixed time, and $g,u_0$ are given ...