一类非线性拟抛物方程的初边值问题

The Initial Boundary Value Problem on a Class of Nonlinear Pseudo parabolic Equations

考虑一类非线性拟抛物方程ｕｔ－ｕｘｘｔ＋ｆ（ｕ）－ｇ（ｕｘ）ｘ＝ｈ（ｘ，ｔ）的初边值问题．证明了整体强解的存在唯一性，并讨论了对应非负初值解的非负性、正则性、渐近性及爆破问题．

The initial boundary value problem on a class of pseudoparabolic equationsu t-u xxt +f(u)-g(u x) x=h(x,t)is considered in this paper.The existence and uniqueness of a global strong solution are obtained.The nonnegativity of the solution corresponding to the nonnegative initial value,the regularity,asymptotic behavior and blow up of solutions are also discussed.