Abstract
<p style='text-indent:20px;'>In this paper, we consider a family of parabolic systems with singular nonlinearities. We study the classification of global existence and quenching of solutions according to parameters and initial data. Furthermore, the rate of the convergence of the global solutions to the minimal steady state is given. Due to the lack of variational characterization of the first eigenvalue to the linearized elliptic problem associated with our parabolic system, some new ideas and techniques are introduced.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Analysis,General Medicine
Reference21 articles.
1. Q. Y. Dai, Y. G. Gu.Quenching phenomena for systems of semilinear parabolic equations, I, Syst. Sci. Math. Sci., 10 (1997), 361-371.
2. J. M. do Ó, R. Clemente.On lane-emden systems with singular nonlinearities and applications to MEMS, Adv. Nonlinear Stud., 18 (2018), 41-53.
3. P. Esposito, N. Ghoussoub and Y. J. Guo, Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS, New York, Courant Lect. Notes Math., Courant Institute of Mathematical Sciences, New York University, 2010.
4. S. Filippas, J. S. Guo.Quenching profiles for one-dimensional semilinear heat equations, Quart. Appl. Math., 51 (1993), 713-729.
5. H. Fujita.On the nonlinear equations ${\Delta} u+e^u = 0$ and ${\partial v}/{\partial t} = {\Delta} v+e^v$, Bull. Amer. Math. Soc., 75 (1969), 132-135.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献