Year: 1997
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 3 : pp. 275–283
Abstract
M. Bertsch & R. Dal Passo proved the existence and uniqueness of the Cauchy problem for u_t = (φ(u),ψ(u_x))_x, where φ > 0, ψ is a strictly increasing function with lim_{s → ∞}ψ(s) = ψ_∞ < ∞. The regularity of the solution has been obtained under the condition φ" < 0 or φ = const. In the present paper, under the condition φ" ≤ 0, we give some regularity results. We show that the solution can be classical after a finite time. Further, under the condition φ" ≤ -α_0 (where -α_0 is a constant), we prove the gradient of the solution converges to zero uniformly with respect to x as t → +∞.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1997-JPDE-5597
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 3 : pp. 275–283
Published online: 1997-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Strongly degenerate parabolic equation