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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 equation
lifespan
classical solution
blow-up
Issue Date: 2003
Publisher: Università degli Studi di Trieste. Dipartimento di Matematica e Informatica
Citation: 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.
URI: http://hdl.handle.net/10077/4194
ISSN: 0049-4704
MS Classification: 35L70
35B05
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.35 (2003)

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