The Cauchy problem for a quasilinear parabolic equation with a large initial gradient and low viscosity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 699-706
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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.
@article{ZVMMF_2010_50_4_a7,
author = {S. V. Zakharov},
title = {The {Cauchy} problem for a quasilinear parabolic equation with a large initial gradient and low viscosity},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {699--706},
publisher = {mathdoc},
volume = {50},
number = {4},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a7/}
}
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S. V. Zakharov. The Cauchy problem for a quasilinear parabolic equation with a large initial gradient and low viscosity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 699-706. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a7/