一类非线性色散型发展方程的反问题

THE INVERSE PROBLEM FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS OF DISPERSIVE TYPE

具有主部ut-uxxt的伪抛物型方程近些年来已引起广泛注意,因为这类方程有着明显的物理背景。众所周知,形如ut+ux+uux-uxxt=0的方程是研究小振幅长波的数学模型,并由T.B.Benjamin,J.L.Bona和J.J.

In this paper we reduce the initial-boundary problem for the pseudo-parabolic equation to Cauchy problem of nonlinear evolution equation.Using the semigroup method we establish the existence and uniqueness of the solution of the inverse problem for the evolution equation and apply this result to the pseudo-parabolic equation.