Abstract
In this paper, the long-time behavior and blowup of solutions for two generalized Ginzburg–Landau type equations with several nonlinear source terms are investigated. First, the conditions in which the solutions of the two equations are positive are analyzed by using Green’s function. According to the characteristics of nonlinear terms, four different functionals are constructed for solving the problems. Finally, we obtain the long-time behavior and finite-time blowup of solutions for the initial and boundary value problem by using these functionals.
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