Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity

作者：Furioli Giulia; Kawakami Tatsuki^*; Ruf Bernhard; Terraneo Elide

来源：Journal of Differential Equations, 2017, 262(1): 145-180.

DOI：10.1016/j.jde.2016.09.024

• Asymptotic behavior
• Nonlinear heat equation
• Fractional diffusion equation
• Exponential nonlinearity
• Orlicz space

We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and mild solutions, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.

• 出版日期2017-1-5