An Analogue of the d’Alembert Formula for the Gurtin-Pipkin Equation with Multipoint Boundary Conditions for Zero Initial Data
摘要
The paper presents the derivation of an analogue of the d’Alembert formula for the Gurtin-Pipkin equation with inhomogeneous multipoint conditions. As a consequence, it is possible to obtain a statement about the possibility or impossibility of reaching a predetermined final regime in a fixed time, when the average temperature at a finite number of points acts as a control.