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STRONG-VISCOSITY SOLUTIONS: SEMILINEAR PARABOLIC PDEs AND PATH-DEPENDENT PDEs

Abstract : The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the standard definition of viscosity solution. Afterwards, we extend the concept of strong-viscosity solution to the case of semilinear parabolic path-dependent partial differential equations, providing an existence and uniqueness result.
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01145301
Contributor : Francesco Russo Connect in order to contact the contributor
Submitted on : Thursday, April 23, 2015 - 5:28:52 PM
Last modification on : Thursday, March 26, 2020 - 9:14:34 PM
Long-term archiving on: : Monday, September 14, 2015 - 1:01:45 PM

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  • HAL Id : hal-01145301, version 1
  • ARXIV : 1505.02927

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Andrea Cosso, Francesco Russo. STRONG-VISCOSITY SOLUTIONS: SEMILINEAR PARABOLIC PDEs AND PATH-DEPENDENT PDEs. 2015. ⟨hal-01145301v1⟩

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