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Journal Articles Osaka Journal of Mathematics Year : 2019

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

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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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Dates and versions

hal-01145301 , version 1 (23-04-2015)
hal-01145301 , version 2 (17-11-2018)
hal-01145301 , version 3 (08-03-2019)

Identifiers

  • HAL Id : hal-01145301 , version 3

Cite

Andrea Cosso, Francesco Russo. STRONG-VISCOSITY SOLUTIONS: SEMILINEAR PARABOLIC PDEs AND PATH-DEPENDENT PDEs. Osaka Journal of Mathematics, 2019, 56 (2), pp.323-373. ⟨hal-01145301v3⟩
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