(untitled) (Journal of Partial Differential Equations, 1990)
We first consider the initial value problem of nonlinear Schr&#246dinger equation with the effect of dissipation, and prove the existence of global generalized solution and smooth solution as some conditions respectively. Secondly, we disscuss the asymptotic behavior of solution of mixed problem in bounded domain for above equation. Thirdly, we find the &#8220blow up&#8221 phenomenon of the solution of mixed problem for equation iu_t = &#916u + &#946f(|u|&sup2)u - i&#978(t)2u, x &#8712 &#937 &#8834 R&sup3, t > 0 i. e. there exists T_0 > 0 such that lim^t&#8594&#915_0 || &#8711u || &sup2_L_t(&#937) = &#8734. The main means are a prior estimates on fractional degree Sobolev space, related properties of operator’s semigroup and some integral identities.