Backward Diffusion-Wave Problem: Stability, Regularization, and Approximation

Data regularization for a backward time-fractional diffusion problem

A regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...

A Nonhomogeneous Backward Heat Problem: Regularization and Error Estimates

We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation ut − uxx = f(x, t), (x, t) ∈ (0, π)× (0, T ), u(0, t) = u(π, t) = 0, (x, t) ∈ (0, π)× (0, T ). This problem is known as the backward heat problem and is severely ill-posed. Our goal is to present a simple and convenient regularization method, and sharp error estimates for ...

Problem of Rayleigh Wave Propagation in Thermoelastic Diffusion

In this work, the problem of Rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. The formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, isoconcentrated boundary. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obt...

Approximation of Fractional Diffusion-wave Equation

In this paper we consider the solution of the fractional differential equations. In particular, we consider the numerical solution of the fractional one dimensional diffusion-wave equation. Some improvements of computational algorithms are suggested. The considerations have been illustrated by examples.