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

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• 作者：Giulia Furioli^a ; ^{gfurioli@unibg.it" class="auth_mail" title="E-mail the corresponding author} ; Tatsuki Kawakami^b ; ^{kawakami@ms.osakafu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Bernhard Ruf^c ; ^{bernhard.ruf@unimi.it" class="auth_mail" title="E-mail the corresponding author} ; Elide Terraneo^c ; ^{elide.terraneo@unimi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Asymptotic behavior ; Nonlinear heat equation ; Fractional diffusion equation ; Exponential nonlinearity ; Orlicz space
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 January 2017
• 年：2017
• 卷：262
• 期：1
• 页码：145-180
• 全文大小：445 K

文摘

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.