TY - JOUR
T1 - Fractal Burgers Equations
AU - Biler, Piotr
AU - Funaki, Tadahisa
AU - Woyczynski, Wojbor A.
N1 - Funding Information:
Part of this research was carried out while the first-named author was a research scholar at the CWRU Center for Stochastic and Chaotic Processes in Science and Technology (Fall 1996). Grant support from KBN, ONR, JSPS and NSF is also gratefully acknowledged.
PY - 1998/9/1
Y1 - 1998/9/1
N2 - 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.
AB - 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.
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U2 - 10.1006/jdeq.1998.3458
DO - 10.1006/jdeq.1998.3458
M3 - Article
AN - SCOPUS:0002015456
SN - 0022-0396
VL - 148
SP - 9
EP - 46
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -