Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation.
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...
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...
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear differential equations of first order. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation, provide an explicit example...
In this paper, we study some finite volume schemes for the nonlinear hyperbolic equation with the initial condition . Passing to the limit in these schemes, we prove the existence of an entropy solution . Proving also uniqueness, we obtain the convergence of the finite volume approximation to the entropy solution in , 1 ≤ p ≤ +∞. Furthermore, if , we show that , which leads to an “” error estimate between the approximate and the entropy solutions (where h defines the size of the...