The Researches Of Properties Of Solutions For Wave Equation With Special Boundary Condition

For the development of our society, people began study complex natural phenomenon and solve complex engineering problems. Recently, waves equations with boundary condi-tions have been treated by many authors. Such as, the linear wave equations and nonlinear wave equations,wave equations with spcial boundary conditions and so on. In this thesis, we study the wave equation with different boundary conditions.The first question we studied is blow-up of solutions for the wave equation with source and boundary damping terms and varied coefficient. We use energy equations get the blow-up of solutions and its uptime. The second question is wave equations of memory type with source terms and acoustic boundary conditions, use Lyapunov function proves the decay of the solution. The third question is blow-up of solution for the wave equations with source and boundary feedback We use energy equations get the blow-up of solutions.