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In nature , many natural phenomena can be studied using partial differential equations , and many dynamic phenomena influenced by the past history of one or more variables we consider here the convolution items hyperbolic wave equation this paper to count , and elaborated in recent years, some scholars , the mathematical methods they used , and the main results obtained , the main existence and the existence of the attractor of the overall solution of such equations are introduced . semigroup theory as memory items damped wave equation under the boundary and initial conditions , the solution of the whole attractor existence where Q is a bounded domain in Rn with smooth boundary , a gt; 0.g (t) is positive on behalf of the memory for nuclear function , and to meet certain conditions , will be introduced later , especially specific research contents are as follows : first , a brief has the memory entries development equation research at home and abroad the status quo , and research directions ; second, given some basic definitions , lemmas and assumptions on the part of the symbol in this article briefly ; , use the Faedo-Garlerkin method simple proof of the system ( 1.2.1 ) - ( 1.2.3 ) the overall solution existence and uniqueness; fourth , to prove to the semigroup theory to understand semigroup existence of global attractor ; fifth, the research for the future evolution equations with memory items a certain outlook .
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