Search

In this paper, we prove that the Cauchy problem for a non-linear wave equation (1)has a unique global generalized solutions in and a unique global classical solution in . We also prove that the Cauchy problem for the equation (1) admits a unique global generalized solution in C2([0, ∞); Wm, p(R) ∩ L∞(R))(m ≥ 0 is an integer,1 ≤ p ≤ ∞) and a unique global classical solution in . [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the existence and uniqueness of the global generalized solution and the global classical solution, the blowup of the solution and the energy decay of the solutions of the initial–boundary value problems for a class of nonlinear wave equations. [Copyright &y& Elsevier]

Abstract: In this paper, the existence and uniqueness of the local generalized solution and the local classical solution for the initial boundary value problem of the quasi-linear wave equation with viscous damping are proved. The nonexistence of the global solution for this problem is discussed by an ordinary differential inequality. Finally, an example is given. [Copyright &y& Elsevier]

In this paper, the global existence of solutions to the initial boundary value problem for a class of quasi-linear wave equations with viscous damping and source terms is studied by using a combination of Galerkin approximations, compactness, and monotonicity methods. [Copyright &y& Elsevier]