Stable estimates for source solution of critical fractal Burgers equation. (January 2016)

• Record Type: Journal Article
• Authors: Jakubowski, Tomasz; Serafin, Grzegorz
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 396
• Page End: 407
• Publication Date: 2016-01
• Subjects: Fractional Laplacian -- Critical Burgers equation -- Source solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.10.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we provide two-sided estimates for the source solution of d -dimensional critical fractal Burgers equation u t − Δ α / 2 + b ⋅ ∇ ( u | u | q ) = 0, q = ( α − 1 ) / d, α ∈ ( 1, 2 ), b ∈ R d, by the density function of the isotropic α -stable process.