Theoretical and practical aspects of heating equation

  • Authors:
  • Marius-Constantin Popescu;Valentina E. Balas;Gheorghe Manolea;Liliana Perescu-Popescu;Nikos Mastorakis

  • Affiliations:
  • Faculty of Electromechanical and Environmental Engineering, University of Craiova, Romania;Faculty of Engineering, "Aurel Vlaicu" University of Arad, Romania;Faculty of Electromechanical and Environmental Engineering, University of Craiova, Romania;"Elena Cuza" College of Craiova, Romania;Technical University of Sofia, Bulgaria

  • Venue:
  • WSEAS Transactions on Systems and Control
  • Year:
  • 2009

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Abstract

We are interested in a null controllability problem for a class of strongly degenerate heat equations. Heat equation parameters are represented graphically (temperature, heat flux) for a particular situation. Then, first for all T 0, we prove a regional null controllability result at time T at least in the region where the equation is not degenerate. The proof is based on an adequate observability inequality for the homogeneous adjoint problem. This inequality is obtained by application of Carleman estimates combined with the introduction of cut-off functions. Then we improve this result: for all T′ T, we obtain a result of persistent regional null controllability during the time interval [T,T]. We give similar results for the (non degenerate) heat equation in unbounded domain. Analysis by numerical simulation of the heating room space has highlighted that the use of composite materials instead of the usual materials of construction is more advantageous in terms of achieving the microclimate conditions, making possible, within certain limits of temperature exterior, a passive air conditioning, which involves reducing energy consumption.