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existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium

Cristelle Barillon, Georgy M. Makhviladze, Vitaly A. Volpert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper is devoted to analysis of an elliptic-algebraic system of equations describing heat explosion in a two phase medium filling a star-shaped domain. Three types of solutions are found: classical, critical and multivalued. Regularity of solutions is studied as well as their behavior depending on the size of the domain and on the coefficient of heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.

Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems

Cheng-Zhong Xu, Gauthier Sallet (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is...

Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

Cheng-Zhong Xu, Gauthier Sallet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system...

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