The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem
as p → + ∞, where Ω is a bounded domain, and b(x) is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.
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In honor of the scientific heritage of Jacques-Louis Lions
Project supported by Fundação para a Ciência e a Tecnologia (FCT) (No. PEst OE/MAT/UI0209/2011). The second author was also supported by an FCT grant (No. SFRH/BPD/69314/201).
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Rodrigues, J.F., Tavares, H. Increasing powers in a degenerate parabolic logistic equation. Chin. Ann. Math. Ser. B 34, 277–294 (2013). https://doi.org/10.1007/s11401-013-0762-3
- Parabolic logistic equation
- Obstacle problem
- Positive solution
- Increasing power
- Subsolution and supersolution
2000 MR Subject Classification