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.
Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity / G. Furioli, T. Kawakami, B. Ruf, E. Terraneo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 262:1(2017 Jan 05), pp. 145-180. [10.1016/j.jde.2016.09.024]
Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity
B. Ruf;E. Terraneo
2017
Abstract
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.
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