Nonlinear hyperbolic equations with small viscosity (Q1111078)

The paper is dedicated to solving the initial value problem for nonlinear partial differential equations of hyperbolic type with the small parameter \(\mu\). The solution in question is sought in the form of asymptotic series in powers of parameter \(\mu\). A few theorems about sufficient conditions for existence of solution of the Cauchy problem are proved. Some a priori estimates of the solutions are obtained. Some results are extended to the Cauchy problem for systems of differential equations. As an example the initial value problem is considered for the Navier-Stokes equation under small viscosity. The references, 28 in number, fully cover the stated problem.