On the KPZ equation with fractional diffusion: global regularity and existence results

2019/04/09 by Abdellaoui, Boumediene, Peral, Ireneo, Primo, Ana +1 · 2 citations
#35K59 #47G20 #47J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.04593

Abstract

In this work we analyze the existence of solutions to the fractional quasilinear problem, (P) \ u_t+(-Δ)^s u · amp;= · amp;|∇ u|^α+ f · amp;\inn Ω_T≡Ω× (0,T),
u(x,t) · amp;= · amp;0 · amp; \inn(ℝ^N∖Ω)× [0,T),
u(x,0) · amp;= · amp;u₀(x) · amp; \innΩ,. where Ω is a C^1,1 bounded domain in ℝ^N, N> 2s and (1)/(2)\dfrac11-s. This behavior clearly exhibits a deep difference with the local case.

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