The influence of data regularity in the critical exponent for a class of semilinear evolution equations

2020 ◽  
Vol 27 (5) ◽  
Author(s):  
Marcelo R. Ebert ◽  
Cleverson R. da Luz ◽  
Maíra F. G. Palma
Keyword(s):  
Critical Exponent ◽  
Evolution Equations ◽  
Semilinear Evolution Equations

scholarly journals Asymptotic Smoothing and Global Attractors for a Class of Nonlinear Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yongqin Xie ◽  
Zhufang He ◽  
Chen Xi ◽  
Zheng Jun
Keyword(s):  
Evolution Equations ◽  
Global Solutions ◽  
Global Attractors ◽  
Nonlinear Evolution Equations ◽  
Time Behavior ◽  
Asymptotic Regularity ◽  
Compact Attractor ◽  
Long Time ◽  
Critical Exponential Growth ◽  
Semilinear Evolution Equations

We prove the asymptotic regularity of global solutions for a class of semilinear evolution equations in H01(Ω)×H01(Ω). Moreover, we study the long-time behavior of the solutions. It is proved that, under the natural assumptions, these equations possess the compact attractor 𝒜 which is bounded in H2(Ω)×H2(Ω), where the nonlinear term f satisfies a critical exponential growth condition.

scholarly journals Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 792-805
Author(s):  
Junfei Cao ◽  
Zaitang Huang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Initial Conditions ◽  
Asymptotically Periodic ◽  
Semilinear Evolution Equations ◽  
Asymptotically Periodic Solutions

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

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