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Comparison and stability of solutions to a class of quasilinear parabolic problems. (English) Zbl 0669.35052

This paper presents new comparison and uniqueness results for the solution of parabolic quasilinear boundary value problems with (and without) obstacles. A stability result in \(L^ 1(\Omega)\) yields the asymptotic stabilisation in this space, when \(t\to +\infty\), towards the corresponding elliptic problem.
Reviewer: M.Chipot

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B35 Stability in context of PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35K20 Initial-boundary value problems for second-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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References:

[1] DOI: 10.1007/BF00248414 · Zbl 0311.35046 · doi:10.1007/BF00248414
[2] Rodrigues, Rend. Mat. 4 pp 458– (1984)
[3] Lions, Quelques-méthodes de résolution des problèmes aux limites non linéaires (1969)
[4] Artola, Boll. Un. Mat. Ital 5 pp 51– (1986)
[5] DOI: 10.1016/0362-546X(82)90050-5 · Zbl 0489.49006 · doi:10.1016/0362-546X(82)90050-5
[6] Chipot, Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities. (1987)
[7] Carrillo, Proc. Roy. Soc. Edinburgh Sect. A 100 pp 281– (1985) · Zbl 0586.35044 · doi:10.1017/S0308210500013822
[8] DOI: 10.1007/BF00250528 · Zbl 0237.49005 · doi:10.1007/BF00250528
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