Existence and nonexistence of global solutions of degenerate and singular parabolic systems

Towards a Unified Approach to Nonexistence of Solutions for a Class of Differential Inequalities

“…We now consider some examples where we can apply Theorem 3.5 and refer the interested reader to [5] and [10] for more applications of the method of test function to different classes of quasilinear evolution inequalities.…”

Pointwise bounds and blow-up for systems of semilinear parabolic inequalities and nonlinear heat potential estimates

“…However, very little attention has been paid to systems of parabolic inequalities, and, as far as we know, all results deal with a very different aspect of these inequalities; namely the nonexistence of global solutions. See for example [3,4,10].…”

Non-Existence of Global Solutions for Higher-Order Evolution Inequalities in Unbounded Cone-Like Domains

“…We want to draw the reader's attention to the fact that many authors use the test function method, and a number of non-existence results are obtained. We mention here the papers [32], [34] by Mitidieri and Pohozaev,[21] by Kurta,[12] by Galakhov,[17], [18] by Kartsatos and Kurta,[4] by Bidaut-Veron and Pohozaev, [7] by Caristi (elliptic inequalities), [47] by Zhang, [3] by Bandle, Levine and Zhang, [6] by Caristi, [10] by Egorov et al, [30] by Levine and Zhang,[40], [41] by Pohozaev and Tesei, [35] by Mitidieri and Pohozaev,[14] by Guedda and Kirane (parabolic inequalities), [43], [42] by Pohozaev and Veron, [36] by Mitidieri and Pohozaev,and [48] by Zhang (hyperbolic inequalities).…”