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arXiv · 1610.06726

Quasilinear generalized parabolic Anderson model equation

Ismael Bailleul·Arnaud Debussche·Martina Hofmanova
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Abstract

We present in this note a local in time well-posedness result for the singular $2$-dimensional quasilinear generalized parabolic Anderson model equation $$ \partial_t u - a(u)\Delta u = g(u)\xi $$ The key idea of our approach is a simple transformation of the equation which allows to treat the problem as a semilinear problem. The analysis is done within the elementary setting of paracontrolled calculus.

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Ismael Bailleul, Arnaud Debussche, Martina Hofmanova. 2016-10-21. Quasilinear generalized parabolic Anderson model equation. https://arxiv.org/abs/1610.06726

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