This article is cited in 11 papers

The Cauchy problem for a quasilinear parabolic equation with a large initial gradient and low viscosity

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219 Russia

Abstract: The Cauchy problem for a quasilinear parabolic equation with a small parameter $\varepsilon$ multiplying the highest derivative is considered. The derivative of the initial function is on the order of $O(1/\rho)$, where $\rho$ is another small parameter. Asymptotic expansions of the solution in powers of $\varepsilon$ and $\rho$ are constructed in various forms.

Key words: Cauchy problem, quasilinear parabolic equation, small parameter multiplying the highest derivative, asymptotic expansion in small parameters.

UDC: 519.633

Received: 26.10.2009

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:4, 665–672

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