Abstract
We show that any global nonnegative and bounded solution to the degenerate parabolic problemut-Δum+f(u)=0 qquad {\rm on} quad Ώ⊂ RN,u|{∂Ώ}=0converges to a single stationary state as time goes to infinity. Here m>0, f is a restriction of a real analytic function defined on a sector containing the half-line [0, ∞), and f(u 1/m) is a continuously differentiable function of u.
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Feireisl, E., Simondon, F. Convergence for Semilinear Degenerate Parabolic Equations in Several Space Dimensions. Journal of Dynamics and Differential Equations 12, 647–673 (2000). https://doi.org/10.1023/A:1026467729263
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DOI: https://doi.org/10.1023/A:1026467729263