Decay estimates of solutions for dissipative wave equations in R^N with lower power nonlinearities

By Ryo Ikehata, Y. Miyaoka, T. Nakatake. 2004

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A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations (2017, methodology): “By only assuming data in Sobolev spaces, the existence result was proved in space dimension n = 1 , 2 in [25], by using energy methods, and in space dimension n ≤ 5 in [38], by using L r − L q estimates, 1 ≤ r ≤ q ≤ ∞ .”
Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application (2003, background): “Recently, Ikehata, Miyaoka and Nakatake [ 11 ] have obtained the global existence of the weak solution to (1.20) and its decay order when 2 11 ,16,19] etc.”
Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “See also Ikehata et al. [18], Ikehata and Tanizawa [17], Ono [29,30], Gallay and Raugel [7,8], Karch [20], and references therein for the global existence and its proﬁle.”