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Browsing by Subject "viscosity solutions"

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    Item type:Article, Access status: Open Access ,
    On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument
    (2014) Topolski, Krzysztof A.
    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 regularization process.