Cauchy Problem For Quasi-linear Wave Equations

This paper consists of three chapters.The first chapter is the introduction.In the second chapter,we will study the existence and uniqueness of the global generalized solution to the Cauchy problem for a class of nonlinear evolution equations with nonlinear damping and source terms.In the third chapter,we will prove the blow-up of solution to the problem mentioned in chapter two and give an example.In the second chapter,we study the following Cauchy problem for a class of nonlinear evolution equationsFor this purpose,we first consider the periodic boundary value problem of the equation (0.1) where x + 2Le_i = (x₁,..., x_i-1, x_i + 2L, x_i+1,..., x_N), L > 0 is a real number.After the existence of the global weak solution to the problem (0.1)-(0.3) are proved, using the sequence of the periodic boundary value problem we prove that the existence of the global weak solution to the Cauchy problem (0.1)-(0.2).Moreover,we can get the existence and uniqueness of the global generalized solution to the problem (0.1)-(0.2) under the condition of the space dimension N = 1.The main results are the fowllowing:Theorem 1 Suppose thatwhere...