On the nonextendable solution and blow-up of the solution of the one-dimensional equation of ion-sound waves in a plasma

The initial boundary-value problem for the equation of ion-sound waves in a plasma is studied. A theorem on the nonextendable solution is proved. Sufficient conditions for the blow-up of the solution in finite time and the upper bound for the blow-up time are obtained using the method of test functions. © 2017, Pleiades Publishing, Ltd.