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Critical Exponent for the Semilinear Wave Equation with Scale Invariant Damping

  • Yuta WakasugiEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper we consider the critical exponent problem for the semilinear damped wave equation with time-dependent coefficients. We treat the scale invariant cases. In this case the asymptotic behavior of the solution is very delicate and the size of coefficient plays an essential role. We shall prove that if the power of the nonlinearity is greater than the Fujita exponent, then there exists a unique global solution with small data, provided that the size of the coefficient is sufficiently large. We shall also prove some blow-up results even in the case that the coefficient is sufficiently small.

Keywords

Damped wave equation time dependent coefficient scale invariant damping critical exponent 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonaka, OsakaJapan

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