On uniqueness for evolution problems with hysteresis. (English) Zbl 0701.35009

Hilpert, Martin

Mathematical models for phase change problems, Proc. Eur. Workshop, Óbidos/Port. 1988, ISNM, Int. Ser. Numer. Math. 88, 377-388 (1989).

[For the entire collection see Zbl 0676.00021.]
A comparison result for regular solutions of the parabolic equation \((u+w)_ t+Au=f\) where w(u) is some hysteresis functional is given which implies uniqueness and stability of solutions.

Reviewer: G.Boillat

MSC:

35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations
35A07	Local existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

comparison result; regular solutions; hysteresis; uniqueness; stability