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Limiting behavior of solutions of \(u_ t=\Delta{} u^ m\;as\;m\rightarrow{} \infty\)

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Publication:1176416
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DOI10.1216/rmjm/1181072966zbMath0737.35002OpenAlexW2024566112MaRDI QIDQ1176416

Paul E. Sacks

Publication date: 25 June 1992

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072966

zbMATH Keywords

porous medium equationlimiting behavior


Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)


Related Items

Singular limit of solutions of the generalized p-Laplacian equation, Singular limit of solutions of the \(p\)-Laplacian equation



Cites Work

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  • On the Mesa problem
  • A singular limit problem for the porous medium equation
  • On a semilinear equation in ℝ2involving bounded measures
  • Asymptotic behaviour of solutions of hyperbolic conservation laws ut + (um)x = 0 as m → ∞ with inconsistent initial values
  • The Mesa Problem: Diffusion Patterns for ut = ∇ · (um∇u) as m → +∞
  • Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
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