Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation (Q1811870)

The authors consider the following parabolic initial-boundary value problem \[ u_t-a(u)u_{xx}-b(u) u_x^2-\lambda \sigma(u)=f(x),\qquad x\in\Omega,\;t>0, \] \[ u(x,0)=u_0(x),\qquad u|_{\partial\Omega}=0,\quad t>0, \] where \(\Omega\) is an open bounded interval in \(\mathbb R.\) There are obtained some existence and uniquenes results by methods for semibounded evolution equations. It is also shown existence of a global attractor for the corresponding dynamical system.