Contraction-Galerkin method for a semi-linear wave equation (Q974423)

The paper gives the existence of the unique weak solution to the initial value problem for the equation \((a(x,t)u_{t})_{t}-(b(x,t)u_{x})_{x}+\lambda F(u)+K| u_{t}| ^{\beta}u_{t}=f(x,t)\) and special mixed boundary conditions, where \(K\) is either zero or a positive constant. The procedure of the proofs is the Galerkin and the contracting methods.