Regular regions for the heat equation

Regular Linear Systems Governed by a Boundary Controlled Heat Equation

In this paper we consider a class of distributed parameter systems governed by the heat equation on bounded domains in Rn. We consider two types of boundary inputs (actuators) and two types of boundary outputs (sensors). Allowing for any possible pairing of these, we consider a total of four possible arrangements of our system. The first type of input (control) is through the Neumann boundary c...

Solution for the Heat Equation

The enclosure method for the heat equation

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary value problems whose governing equation is the heat equation is considered. An explicit method to extract an approximation of the value of the support function a...

The Heat Equation

Backward uniqueness for the heat equation

According to Gurarii and Matsaev [5], these properties are equivalent, but no proof was ever published. Here is a summary of known results. When n = 1, both properties hold if and only if D is a bounded interval. For PII this is evident, for PI this follows from the results of Tychonov [7]. When n = 2, and D is an angular sector {z : | arg z| < α}, the property PII holds if and only if α < 45◦....