Wir nutzen die Transformations Eigenschaften und die integralen Invarianten der porösen Mediumgleichung in m Dimensionen, um ein Lyapunov-Funktional zu konstruieren, das die Entwicklung des Profils zu seiner selbstähnlichen Lösung charakterisiert.

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William I. Newman (Mon,) untersuchte diese Frage.

synapsesocial.com/papers/6a04232b85f419498a2cce76 https://doi.org/https://doi.org/10.1063/1.526028

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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1The asymptotic behaviour of the solution of the filtration equation1973 · 122 citations
2Similarity, Self-Similarity and Intermediate Asymptotics1981 · 561 citations
3Similarity Methods for Differential Equations1974 · 1,303 citations
4A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. II1984 · 73 citations
5Physics of shock waves and high-temperature hydrodynamic phenomena1970 · 4,244 citations