THE 3RD-ORDER NONLINEAR EVOLUTION EQUATION GOVERNING WAVE-PROPAGATIONIN RELAXING MEDIA

Initial value problem for the third-order nonlinear evolution equation governing wave propagation in relaxing media is considered for the ca se of two space dimensions and small initial data. Existence and uniqu eness of the classical solution is established and the solution itself is constructed in the form of a series in the small parameter present in the initial conditions. Long time asymptotic representation is fou nd, which shows that the nonlinearity does not contribute to its major term, The latter consists of mio parts corresponding to isotropic and nonisotropic transfer of small perturbations in space.