ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Local parametric identifiability of parabolic Equations by various discretizations


N. A. Bodunov

Saint-Petersburg Electrotechnical University "LETI",
Department of mathematics № 1,
5 Prof. Popova, Saint-Petersburg,
197376, Russia,


The problem of local parametric identifiability for a semilinear parabolic equation with a scalar parameter is considered. Sufficient conditions of local parametric identifiability are given for the following two approaches: (i) we observe a discretization of an exact solution, and (ii) we observe an approximate solution generated by a discretization of the exact equation.

The discretization of exact solution is observed at growing time moments with increasing accuracy in the phase space. It is shown that given sufficient conditions of local parametric identifiability can be checked for the Chaffee-Infante problem. In the case of a discretization of the exact equation we do not have to refine the observations as time grows.

For both cases it is shown that local parametric identifiability holds for a solution with initial values from an open and dense subset of the phase space.

In this article differential equation with constant delay are considered. For this equation bifurcation of birth of periodic solutions from the balance point are investigated. The base for construction of ramification equation is a special integral equation. New procedure of derivation of integral equation which use special boundary problems for systems of ordinary differential equations are proposed. The Modification of Hopf method is used in order to analyze a system of ramification equations. The conditions of existence and stability are obtained.

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