Global existence and blow-up of solutions for some hyperbolic systems with damping and source terms

Global Well-Posedness for a Class of Kirchhoff-Type Wave System

“…Additionally, Liu and Wang [36] considered the following nonlinear hyperbolic systems with damping and source terms…”

“…The author defined potential well and the outer manifold of the potential well associated with system (17) and got the global existence in the case of (0) < 1 /2 and discussed the global nonexistence of solutions for problem (1)- (5) in the case of (0) ≤ 0 and (0) < on page 88 of [36]. In [37], (1)- (5) was considered with ≡ 1 and without imposing the memory terms ( = ℎ = 0).…”

“…By reviewing above known results and also [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], we will face the fact that the following unsolved problems arise naturally. Firstly, from [38] we know the global existence for the definitely positive energy, but we know less for the initial energy which may be negative.…”

Global well-posedness for semilinear hyperbolic equations with dissipative term

“…we can find a host of literature [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Recently in [9], problem (1) was studied.…”

Blow-up solutions of cubic differential systems

“…For nonautonomous differential systems problems (i) and (ii) are studied in [1][2][3]. In some other classes of differential equations and systems the blow-up phenomena have been studied by many authors (see, for example, [4][5][6][9][10][11][13][14][15][16][17] and references therein).…”