Fundamental solutions and lacunae of quasihyperbolic equations

This article is devoted to a study of the behaviour of the solution to the Cauchy problem for the quasihyperbolic equation (1) (defined below in §1). For such equations, as we shall show, certain regions inside the base of the characteristic cone can turn out to be lacunae or weak lacunae (defined in §1). Next we show that each quasihyperbolic equation (1) can be regarded as the limit for some hyperbolic equation whose coefficients in the series of higher derivatives in $t$ tend to zero. We establish a connection between fundamental solutions to the Cauchy problem for both equations. The statements of the main results have been published in [1].