On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument
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 dif...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2014-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol34/2/art/opuscula_math_3426.pdf |
| Summary: | 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. |
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| ISSN: | 1232-9274 |