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 + 2Lei = (x1,..., xi-1, xi + 2L, xi+1,..., xN), 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...
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