Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations

Existence and Nonexistence of Global Solutions for Higher-Order Nonlinear Viscoelastic Equations

“…At the same time, A. B. Aliev and B. H. Lichaei [1] consider the Cauchy problem for equation in (1.3), and they found the existence and nonexistence criteria of global solutions using the L p -L q estimate for the corresponding linear problem and also established the asymptotic behavior of solutions and their derivatives as t → +∞.…”

Finite difference schemes for the two‐dimensional semilinear wave equation

“…The global existence and other properties of the problem (1)- (3) are proved in Refs. [21][22][23][24][25][26][27][28][29][30]. Numerical approximations of the nonlinear wave equation have been studied by several authors.…”

Degenerate multi-term fractional differential equations in locally convex spaces

“…For further information concerning the wellposedness of Sobolev first order degenerate equations, the reader may consult the monographs by Favini, Yagi [9], Krein [31], Carroll, Showalter [7], Melnikova, Filinkov [34] and Sviridyuk, Fedorov [45], as well as the papers [1, 10-14, 35, 50, 51, 55]. The well-posedness of various types of degenerate Sobolev equations of second order have been analyzed in [2,4,7,9,15,22,36,44,52,56]. The corresponding results on degenerate Sobolev equations with integer higher-order derivatives can be found in [3], [9,Section 5.7], [45][46][47][48][49]56].…”