On higher-order semilinear parabolic equations with measures as initial data

被引：0

作者：

Galaktionov, VA ^{[1
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] MV Keldysh Appl Math Inst, Moscow 125047, Russia

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2004年 / 6卷 / 02期

关键词：

Cauchy problem; semilinear parabolic equation; Dirac mass; existence; nonexistence;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider 2mth-order (m greater than or equal to 2) semilinear parabolic equations u(t) = -(-Delta)(m) u +/-\u\(p-1)u in R-N x R+ (p > 1), with Dirac's mass delta(x) as the initial function. We show that for p < p(0) = 1 + 2m/ N, the Cauchy problem admits a solution u(x, t) which is bounded and smooth for small t > 0, while for p greater than or equal to p(0) such a local in time solution does not exist. This leads to a boundary layer phenomenon in constructing a proper solution via regular approximations.

引用

页码：193 / 205

页数：13

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