FRACTAL BURGERS EQUATIONS

The paper studies local and global in time solutions to a class of mul tidimensional generalized Burgers-type equations with a Fractional pow er of the Laplacian in the principal part and with general algebraic n onlinearity. Such equations naturally appear in continuum mechanics. O ur results include existence; uniqueness, regularity and asymptotic be havior of solutions to the Cauchy problem as well as a construction of self-similar solutions. The role of critical exponents is also explai ned. (C) 1998 Academic Press.