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A class of nonlinear non-classical parabolic equations. (English) Zbl 0702.35120

This paper deals with a class of non-classical parabolic equations in which certain trace-type functionals of the solution are involved. These equations are strongly motivated by a large class of parabolic inverse problems. The paper gives a novel approach to study various parabolic inverse problems. Because of the nonlocal terms in the equations the global existence becomes very difficult.
The maximum principle cannot be applied. The authors use integral estimates and iteration techniques to derive some a priori estimates in one space dimension and establish the global existence under certain conditions. Moreover, the uniqueness and continuous dependence of the solution are also obtained. Some further results are obtained recently by the second author [Appl. Anal. 34, 67-78 (1989; Zbl 0659.35104)].
Reviewer: John R.Cannon

MSC:

35K55 Nonlinear parabolic equations
35R30 Inverse problems for PDEs
35B45 A priori estimates in context of PDEs

Citations:

Zbl 0659.35104
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References:

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