Fractal Hamilton-Jacobi-KPZ equations

2006/01/29 by Karch, Grzegorz, Woyczynski, Wojbor A. · 2 citations
#35B40 #35K55 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.math/0601712

Abstract

Nonlinear and nonlinear evolution equations of the form u_t=Łu ±|∇ u|^q, where Ł is a pseudodifferential operator representing the infinitesimal generator of a Lévy stochastic process, have been derived as models for growing interfaces in the case when the continuous Brownian diffusion surface transport is augmented by a random hopping mechanism. The goal of this paper is to study properties of solutions to this equation resulting from the interplay between the strengths of the "diffusive" linear and "hyperbolic" nonlinear terms, posed in the whole space \bbfR^N, and supplemented with nonnegative, bounded, and sufficiently regular initial conditions.

Cited by

• A Schauder regularity theory for nonlocal and mixed local-nonlocal viscous Hamilton\unicodex2013Jacobi equations
• Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

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