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 th...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 ana- lyzed 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.展开更多
基金This work was supported by the Natural Science Foundation of Anhui Province （1508085MA10）, the Key Program of the Youth Elite Support Plan in Universities of Anhui Province （gxyqZD2016340）, the Key Projects of Suzhou University Outstanding Youth Talent Support Program （2016XQNRL003）.
文摘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 ana- lyzed 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.
