Decay estimates of solutions for dissipative wave equations in RN with lower power nonlinearities

L p -L q estimates of solutions to the damped wave equation in 3-dimensional space and their application

“…Recently, Ikehata, Miyaoka and Nakatake [11] have obtained the global existence of the weak solution to (1.20) and its decay order when 2 < 1 + α < N N −2 (N = 1, 2, 3). Also, they conjecture the global existence of the solution when 2 ≥ 1 + α > 1 + 2 N (N = 3), based on the results by Nishihara [22], Yang and Milani [28].…”

Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

“…IkehataTanizawa [12] consider the global existence part for noncompactly supported data. There are many related results to the so-called di¤usion phenomenon, and we quote some of them below: Han-Milani [4], Ikehata [7], IkehataMiyaoka-Nakatake [8], Ikehata-Nishihara [9], Ikehata-Ohta [11], HosonoOgawa [5], Marcati-Nishihara [20], Nishihara [25,26], Li-Zhou [18], Narazaki [24], Zhang [41], and the references there in.…”

Global Solvability and Lp Decay for the Semilinear Dissipative Wave Equations in Four and Five Dimensions

“…See [9], [18] for f ðuÞ ¼ Àjuj a u and for large data.) Recently, when N ¼ 3, Nishihara [17] has proved a global existence theorem for the initial data ðu 0 ; [7] for N ¼ 1; 2 and a > 2=N, Hosono and Ogawa [6] for N ¼ 2 and a > 2=N, and Marcati and Nishihara [12] for N ¼ 1 and a > 2=N.) On the other side, in [19] we have solved this problem when N a 3 and 2=N < a a 2=ðN À 2Þ þ for the initial data ðu 0 ;…”