*(English)*Zbl 0567.35001

This volume is a valuable contribution to the one-dimensional heat equation. It can serve both as a reference book, as well as a textbook. The author has systematically collected and presented his own research material and that of other research workers, from 1800 to 1982.

He devotes first six chapters in presenting the standard basic material for the heat equation. The exposition is quite systematic and lucid and can be followed by scientists who do not have sufficiently good mathematical background. Some of the interesting topics are topics of free-boundary value problems such as the one-phase Stefan problem, inverse problem, some classes of not-well-posed problems, numerical methods for state-estimation problems and the inhomogeneous heat equation. This volume can be useful for students of mathematics, engineering and physics. It can serve for a variety of courses, such as a course in parabolic partial differential equations, a course in the initial-boundary-value problems for the heat equation, a course in free- boundary-value problems, a course in parameter identification and several others.

##### MSC:

35-01 | Textbooks (partial differential equations) |

35K05 | Heat equation |

35R30 | Inverse problems for PDE |

80A20 | Heat and mass transfer, heat flow |

35B10 | Periodic solutions of PDE |

35C05 | Solutions of PDE in closed form |

35C10 | Series solutions of PDE |

35C15 | Integral representations of solutions of PDE |

35R25 | Improperly posed problems for PDE |

35R35 | Free boundary problems for PDE |