Local Solvability and Decay of the Solution of an Equation with Quadratic Noncoercive Nonlineatity

Abstract

An initial-boundary value problem for plasma ion-sound wave equation is considered. Boltzmann distribution is approximated by a quadratic function. The local (in time) solvability is proved and the analitycal-numerical investigation of the solution's decay is performed for the considered problem. The sucient conditions for solution's decay and an upper bound of the decay moment are obtained by the test function method. In some numerical examples, the estimation is specied by Richardson's mesh renement method. The time interval for numerical modelling is chosen according to the decay moment's analytical upper bound. In return, numerical calculations rene the moment and the spacetime pattern of the decay. Thus, analytical and numerical parts of the investigation amplify each other.