Abstract
We consider the initial-value problem for a quasilinear heat-conduction or diffusion equation with variable density decreasing at infinity. We show that the asymptotic behavior of the given process is self-similar. Indeed, as t → ∞ the solution of the problem approaches a self-similar solution of a certain singular “limit” equation. The limit solution has compact support for any t > 0 and cusp-type shape at the space origin.
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Galaktionov, V.A., Kamin, S., Kersner, R. et al. Intermediate Asymptotics for Inhomogeneous Nonlinear Heat Conduction. Journal of Mathematical Sciences 120, 1277–1294 (2004). https://doi.org/10.1023/B:JOTH.0000016049.94192.aa
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DOI: https://doi.org/10.1023/B:JOTH.0000016049.94192.aa