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Existence, uniqueness and stability of semi-linear rough partial differential equations · arXivDesk

1809.00841Sep 4, 2018

Existence, uniqueness and stability of semi-linear rough partial differential equations

Peter Friz, Torstein Nilssen, Wilhelm Stannat

Abstract

We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on $\mathbb{R}^d$ using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in $L^p(\mathbb{R}^d)$ , and then -- based on a new method -- energy estimates for non-degenerate linear rough PDE's. We accomplish this by controlling the energy in a properly chosen weighted $L^2$

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We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on R^d using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in L^p(R^d), and then -- based on a new method -- energy estimates for non-degenerate linear rough PDE's.

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The paper addresses: Existence, uniqueness and stability of semi-linear rough partial differential equations.
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on R^d using the variational approach.