Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4194
Title: Blow-up for Semilinear Wave Equations with a Data of the Critical Decay having a Small Loss
Authors: Kurokawa, Yuki
Takamura, Hiroyuki
Keywords: semilinear wave equationlifespanclassical solutionblow-up
Issue Date: 2003
Publisher: Università degli Studi di Trieste. Dipartimento di Matematica e Informatica
Source: Yuki Kurokawa and Hiroyuki Takamura, "Blow-up for Semilinear Wave Equations with a Data of the Critical Decay having a Small Loss", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 35 (2003), pp. 165–193.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
35 (2003)
Abstract: 
It is known that we have a global existence for wave
equations with super-critical nonlinearities when the data has a
critical decay of powers. In this paper, we will see that a blow-up
result can be established if the data decays like the critical power
with a small loss such as any logarithmic power. This means that
there is no relation between the critical decay of the initial data
and the integrability of the weight, while the critical power of the
nonlinearity is closely related to the integrability. The critical
decay of the initial data is determined only by scaling invariance
of the equation. We also discuss a nonexistence of local in time
solutions for the initial data increasing at infinity.
Type: Article
URI: http://hdl.handle.net/10077/4194
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.35 (2003)

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