Title of article
On the uniqueness of L1-continuation after blowup
Author/Authors
Noriko Mizoguchi، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2008
Pages
18
From page
2893
To page
2910
Abstract
This paper is concerned with the uniqueness of L1-continuation beyond blowup for a Cauchy problem
of a semilinear heat equation
ut = u +up in RN ×(0, T ),
u(x, 0) = u0(x) 0 inRN
(P)
with p > 1, 0 < T ∞ and u0 ∈ L∞(RN). Here we say that u is an L1-solution of (P) if u ∈
C([0, T );L1
loc(RN)) with u ∈ L
p
loc(RN × (0, T )) satisfies (P) in the distributional sense. In the case of
pS
pJL in the radial case. If for an L1-solution u of (P) there exists a sequence {un} of classical solutions of (P) such that u0,n→u0 in L∞(RN) as n→∞for the sequence {u0,n} of initial data and that un(t)→u(t) in L p loc(RN) as n→∞for t ∈ (0, T ), then u is called a limit L1-solution. Based on the sufficient condition, we prove the uniqueness of limit L1-solution with radial symmetry after blowup for p >pJL. © 2008 Published by Elsevier Inc
Keywords
Continuation , blowup , Braid group theory , Semilinear heat equation
Journal title
Journal of Functional Analysis
Serial Year
2008
Journal title
Journal of Functional Analysis
Record number
839642
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