Critical exponents for semilinear dissipative wave equations in RN

By Ryo Ikehata, Masahito Ohta. 2002

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A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations (2017, background): “…results for p > p 0 and for p > p 1 , proved in Sections 2.2 and 2.4, since (16) Indeed, it is known that the critical exponent for semilinear problems like (1) and (2) changes if the L 1 assumption on the initial data is replaced by an L m assumption, for m ∈ (1 , 2] (see, for instance, [26]).”
New decay estimates for linear damped wave equations and its application to nonlinear problem (2004, unknown): “For the Fujita type problem of (6) in RN , which has non-compactly supported initial data, we refer the reader to Ikehata–Miyaoka–Nakatake [21], Ikehata–Ohta [22], Nakao–Ono [23], and Nishihara [8].”
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “There have been many studies of the non-absorbing semilinear term problem [7,8,13–17,22, 24,31,32,34], etc.”