@Article{Topolski2014,
author = "Topolski, Krzysztof A.",
title = "On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "2",
pages = "425--441",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.2.425",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.2.425",
abstract = "The degenerate parabolic Cauchy problem is considered. A functional argument in the equation is of the Hale type. As a limit of piecewise classical solutions we obtain a viscosity solution of the main problem. Presented method is an adaptation of Tonelli's constructive method to the partial differential-functional equation. It is also shown that this approach can be improved by the vanishing viscosity method and regularisation process.",
keywords = "viscosity solutions, parabolic equation, differential-functional equation",
issn = "1232-9274"
}