Asymptotic behaviour and global existence of solutions for some classes of nonlinear parabolic equations (Q1849322)

The paper deals with the asymptotic behavior and global existence of solutions for some classes of nonlinear parabolic equations in regard to the monotone properties of the nonlinear term. The asymptotic behavior of solutions of the initial-boundary value problem for nonlinear parabolic equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions. Existence of extremal solutions of semilinear elliptic and parabolic equations is investigated via monotone iterative methods. The extremal solutions are obtained via monotone iterates.