TY  - JOUR
ID  - Topolski2014
LB  - Topolski2014
AU  - Topolski, Krzysztof A.
TI  - On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument
ST  - On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 2
SP  - 425
EP  - 441
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.2.425
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.2.425
AB  - 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.
KW  - viscosity solutions
KW  - parabolic equation
KW  - differential-functional equation
SN  - 1232-9274
ER  -