Year: 1997
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 85–96
Abstract
M. Bertsch and R. Dal Passo [1] considered the equation u_t = (φ(u)ψ(u_z))x., where φ > 0 and ψ is a strictly increasing function with lim_{s → ∞} ψ(s) = ψ_∞ < ∞. They have solved the associated Cauchy problem for an increasing initial function. Furthermore, they discussed to what extent the solution behaves like the solution of the first order conservation law u_t = ψ_∞(φ(u))_x. The condition φ > 0 is essential in their paper. In the present paper, we study the above equation under the degenerate condition φ(0) = 0. The solution also possesses some hyperbolic phenomena like those pointed out in [1].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1997-JPDE-5583
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 85–96
Published online: 1997-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Degenerate parabolic equation