The book contains eleven chapters introduced by an introductory description. Qualitative properties for the semilinear dissipative wave equations are discussed in Chapter 2 and Chapter 3 based on the solutions with compactly supported initial data. The purpose of Chapter 4 is to present results according to the well-possednes and behavior f solutions the nonlinear viscoelastic wave equations in weighted spaces. Elements of theory of Kirchhoff problem...