naa a22 4500 510781403 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0038-6 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0038-6 Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations [Elektronische Daten] [Kazuhiro Ishige, Tatsuki Kawakami] This paper is concerned with the Cauchy problem for the nonlinear parabolic equation $${\partial _t}u| = \vartriangle u + F(x,t,u,\nabla u){\text{ in }}{{\text{R}}^N} \times (0,\infty ),{\text{ }}u(x,0) = \varphi (x){\text{ in }}{{\text{R}}^N},$$ , where $$\begin{gathered} N \geqslant 1, \hfill \\ F \in C(R^N \times (0,\infty ) \times R \times R^N ), \hfill \\ \phi \in L^\infty (R^N ) \cap L^1 (R^N ,(1 + |x|^K )dx)forsomeK \geqslant 0 \hfill \\ \end{gathered} $$ . We give a sufficient condition for the solution to behave like a multiple of the Gauss kernel as t → ∞ and obtain the higher order asymptotic expansions of the solution in W 1,q (R N ) with 1 ≤ q ≤ ∞. Hebrew University Magnes Press, 2013 Ishige Kazuhiro Mathematical Institute, Tohoku University, 980-8578, Aoba, Sendai, Japan aut Kawakami Tatsuki Department of Mathematical Sciences, Osaka Prefecture University, 599-8531, Sakai, Japan aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 317-351 0021-7670 121:1<317 2013 121 11854 https://doi.org/10.1007/s11854-013-0038-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0038-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ishige Kazuhiro Mathematical Institute, Tohoku University, 980-8578, Aoba, Sendai, Japan aut NATIONALLICENCE 700 1- Kawakami Tatsuki Department of Mathematical Sciences, Osaka Prefecture University, 599-8531, Sakai, Japan aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 317-351 0021-7670 121:1<317 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer