Some Study Of Wave Equation With Source And Viscoelastic Terms

In this thesis, we considcr the blow-up and decay of solution to wave equation with source and viscoclastic terms.Firstly, we investigate the solutions of viscoclastic equation with nonlinear source blow up under suitable condition, even for vanishing initial energy.Secondly, when the initial energy tends to a constant, the solution blow up.At last, by constructing new function and using elementary inequalities, we prove the decay for this equation.In chapter2, I discuss the following equations: here,7>0,u0,u1are two compactly supported functions and g is a positive nonincrcasing function defined on R+.We first prove the solution of the equation blow up when initial energy tends to zero and a fixed value. In the meantime, we prove the solution decay polynomiallyThe content of chapter3involves a nonlinear viscoclastic equation. While we discuss both of the equations, we use Young inequality, Holder inequality, Sobolev inequality, Integration-by-parts formula, constructing a new function.