## Entropy and Partial Differential EquationsAs well as recent research, this text contains current types of results about positive solutions of linear elliptic and parabolic equations. It should be of interest to mathematicians involved in thermodynamics, and to engineers and physicists, particularly those concerned with heat transfer. |

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### Contents

ENTROPY AND THE HEAT EQUATION | 23 |

CLAUSIUS INEQUALITY AND PARABOLIC | 46 |

AN INEQUALITY ASSOCIATED WITH | 62 |

Copyright | |

3 other sections not shown

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addition algebras analysis appeal applications approximation arbitrarily large argument arrive blog boundary conditions chapter choice Clausius coefficients conclusion corresponding deduce defined depend derivative dimension eigenvalue elliptic entropy entropy balance equation equal estimate exist explicit expressed fact follows formula function Green's theorem hand happens heat balance equation heat equation heat flux heat supply Hence holds identically implies inequality initial condition integral interpret interval introduce l;ajk limit methods n-dimensional namely nonnegative once operators order relation outward parabolic partial differential equations periodic positive constant possible present proved rate of change region restrictions right-hand side satisfies sides solution space sufficiently suppose taken tells temperature theory University upper bound value problem vanishes verify Volume ди ді ду