Quasilinear generalized parabolic Anderson model equation

We present in this note a local in time well-posedness result for the singular 2-dimensional quasilinear generalized parabolic Anderson model equation ∂ t u - a ( u ) Δ u = g ( u ) ξ . The key idea of our approach is a simple transformation of the equation which allows to treat the problem as a semi...

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Veröffentlicht in:	Stochastic partial differential equations : analysis and computations 2019-03, Vol.7 (1), p.40-63
Hauptverfasser:	Bailleul, I., Debussche, A., Hofmanová, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Computational Mathematics and Numerical Analysis Computational Science and Engineering Mathematics Mathematics and Statistics Numerical Analysis Partial Differential Equations Probability Theory and Stochastic Processes Statistical Theory and Methods Two dimensional models Well posed problems
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Beschreibung
Zusammenfassung:	We present in this note a local in time well-posedness result for the singular 2-dimensional quasilinear generalized parabolic Anderson model equation ∂ t u - a ( u ) Δ u = g ( u ) ξ . 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.
ISSN:	2194-0401 2194-041X
DOI:	10.1007/s40072-018-0121-1