Fractal Burgers Equations

Piotr Biler, Tadahisa Funaki, Wojbor A. Woyczynski

Research output: Contribution to journalArticle

141 Citations (Scopus)

Abstract

The paper studies local and global in time solutions to a class of multidimensional generalized Burgers-type equations with a fractional power of the Laplacian in the principal part and with general algebraic nonlinearity. Such equations naturally appear in continuum mechanics. Our results include existence, uniqueness, regularity and asymptotic behavior of solutions to the Cauchy problem as well as a construction of self-similar solutions. The role of critical exponents is also explained.

Original languageEnglish
Pages (from-to)9-46
Number of pages38
JournalJournal of Differential Equations
Volume148
Issue number1
DOIs
Publication statusPublished - 1998 Sep 1
Externally publishedYes

Fingerprint

Burgers Equation
Fractals
Fractal
Continuum mechanics
Fractional Powers
Existence-uniqueness
Continuum Mechanics
Self-similar Solutions
Asymptotic Behavior of Solutions
Critical Exponents
Cauchy Problem
Regularity
Nonlinearity
Class

ASJC Scopus subject areas

  • Analysis

Cite this

Fractal Burgers Equations. / Biler, Piotr; Funaki, Tadahisa; Woyczynski, Wojbor A.

In: Journal of Differential Equations, Vol. 148, No. 1, 01.09.1998, p. 9-46.

Research output: Contribution to journalArticle

Biler, Piotr ; Funaki, Tadahisa ; Woyczynski, Wojbor A. / Fractal Burgers Equations. In: Journal of Differential Equations. 1998 ; Vol. 148, No. 1. pp. 9-46.
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