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. © 1998 Academic Press.
CITATION STYLE
Biler, P., Funaki, T., & Woyczynski, W. A. (1998). Fractal Burgers Equations. Journal of Differential Equations, 148(1), 9–46. https://doi.org/10.1006/jdeq.1998.3458
Mendeley helps you to discover research relevant for your work.