ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF THE CAUCHY PROBLEM FOR NONLINEAR PARABOLIC EQUATIONS

作者：Ishige Kazuhiro^*; Kawakami Tatsuki

来源：Journal d Analyse Mathematique, 2013, 121(1): 317-351.

DOI：10.1007/s11854-013-0038-6

This paper is concerned with the Cauchy problem for the nonlinear parabolic equation %26lt;br%26gt;tu = 1 u + F(x, t, u,. u) in R N x (0,8), u(x, 0) =.(x) in R N, %26lt;br%26gt;where %26lt;br%26gt;N = 1, F. C(R N x (0,8) x R x R N),.. L 8(R N) n L 1 (R N, (1 + | x| K) dx) for some K %26gt;= 0. %26lt;br%26gt;We give a sufficient condition for the solution to behave like a multiple of the Gauss kernel as t -%26gt; a and obtain the higher order asymptotic expansions of the solution in W (1,q) (R (N) ) with 1 a parts per thousand currency sign q a parts per thousand currency sign a infinity.

• 出版日期2013-10