On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

Inverse Problem for a Heat Equation with Piecewise-constant Conductivity

We consider the inverse problem of the identification of a piecewiseconstant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a ”layer peeling” argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorith...

Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 , and Shah and Wiener 2 , usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years, great attention has been paid to the study of the existence of almost-periodic-type soluti...

Identifiability of Piecewise Constant Conductivity in a Heat Conduction Process

We study the identification and identifiability problems for heat conduction in a nonhomogeneous rod. The identifiability results are established for two different sets of observations. Given a sequence of distributed type observations, the identifiability is proved for conductivities in a piecewise smooth class of functions. In the case of observations taken at finitely many points the identif...

Ergodic Type Solutions of Differential Equations with Piecewise Constant Arguments

We summarize the conditions discovered for the existence of new ergodic type solutions (asymptotically almost periodic, pseudo almost periodic, . . .) of differential equations with piecewise constant arguments. Their existence is characterized by introducing a new tool, the ergodic sequences. 2000 Mathematics Subject Classification. 39-02, 34K14, 34D09.

Identifiability of Piecewise Constant Conductivity