Uniqueness of limit flow for a class of quasi-linear parabolic equations

作者：Squassina Marco^*; Watanabe Tatsuya

来源：Advances in Nonlinear Analysis, 2017, 6(2): 243-276.

DOI：10.1515/anona-2016-0134

• Quasilinear parabolic equation
• asymptotic behavior
• omega-limit set
• blow-up

We investigate the issue of uniqueness of the limit flow for a relevant class of quasi-linear parabolic equations defined on the whole space. More precisely, we shall investigate conditions which guarantee that the global solutions decay at infinity uniformly in time and their entire trajectory approaches a single steady state as time goes to infinity. Finally, we obtain a characterization of solutions which blow up, vanish or converge to a stationary state for initial data of the form lambda phi(0) while lambda > 0 crosses a bifurcation value lambda(0.)

• 出版日期2017-5