Fractal Burgers equations (Q1268402)

The theory of generalized Burgers-type equations with a fractional power of the Laplacian in the principal part and with a general algebraic nonlinearity is presented. Such equations naturally appear in continuum mechanics. The given results include existence, uniqueness, regularity, asymptotic behavior of solutions to the Cauchy problem and a construction of self-similar solutions. The role of critical fractal exponents is also discussed. The results presented in the paper are widely compared with those obtained by others authors.