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Improved bounds for some nonstandard problems in generalized heat conduction |
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| Authors: | LE Payne JC Song |
| Institution: | a Department of Mathematics, Cornell University, Ithaca, NY 14853, USA b Department of Mathematics, University of Tennessee, Knoxville, TN 37916, USA c Department of Applied Mathematics, Hanyang University, Ansan, Kyunggido 425-791, South Korea |
| Abstract: | We consider the Maxwell-Cattaneo system of equations for generalized heat conduction where the temperature and heat flux satisfy a nonstandard auxiliary condition which prescribes a combination of their values initially and at a later time. We obtain L2 bounds for the temperature and heat flux by means of Lagrange identities. These bounds extend the range of validity for the parameter in the nonstandard condition under a constraint on the coefficients in the differential equations. |
| Keywords: | Generalized heat conduction Maxwell-Cattaneo system Nonstandard problem |
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