On the blow-up phenomena for a 1-dimensional equation of ion sound waves in a plasma: Analytical and numerical investigation

The initial-boundary value problem for an equation of ion sound waves in plasma is considered. A theorem on nonextendable solution is proved. The blow-up phenomena are studied. The sufficient blow-up conditions and the blow-up time are analysed by the method of the test functions. This analytical a priori information is used in the numerical experiments, which are able to determine the process of the solution's blow-up more accurately.