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A remark on the stability of stationary solutions of parabolic variational inequalities. (English) Zbl 0738.49006

We generalize our former results [Math. Ann. 283, No. 2, 257-270 (1989; Zbl 0642.49006)] concerning the exponential stability of stationary solutions of semilinear parabolic variational inequalities. The usefulness of this generalization is illustrated by three examples.
Reviewer: P.Quittner

MSC:

49J40 Variational inequalities
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
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References:

[1] P. Drábek M. Kučera: Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions. Czechoslovak Math. J. 36 (1986), 116-130. · Zbl 0608.35032
[2] P. Quittner: Bifurcation points and eigenvalues of inequalities of reaction-diffusion type. J. reine angew. Math, 380 (1987), 1-13. · Zbl 0617.35053
[3] P. Quittner: On the principle of linearized stability for variational inequalities. Math. Ann. 283 (1989), 257-270. · Zbl 0642.49006
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