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Zbl 0567.35001
Cannon, John Rozier
The one-dimensional heat equation. Foreword by Felix E. Browder. (English)
[B] Encyclopedia of Mathematics and Its Applications, Vol. 23. Menlo Park, California etc.: Addison-Wesley Publishing Company; Cambridge etc.: Cambridge University Press. XXV, 483 p. (1984).

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. \par 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.
[B.R.Bhonsle]
MSC 2000:
*35-01 Textbooks (partial differential equations)
35K05 Heat equation
35R30 Inverse problems for PDE
80A20 Heat and mass transfer
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

Keywords: one-dimensional heat equation; free-boundary value problems; one-phase Stefan problem; inverse problem; not-well-posed problems; numerical methods; state-estimation problems

Cited in: Zbl 1156.35001

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