Abstract
In this paper, we study the nonexistence of global weak solutions to higher-order time-fractional evolution inequalities with subcritical degeneracy. Using the test function method and some integral estimates, we establish sufficient conditions depending on the parameters of the problems so that global weak solutions cannot exist globally.
Highlights
We are first concerned with the study of the nonexistence of global weak solutions to time-fractional evolution inequalities of the form:
The study of the nonexistence of global solutions to time-fractional evolution equations and inequalities has been initiated by Kirane and their collaborators
Using the integration by parts rule given by Lemma 1, we define global weak solutions to (1)–(2) as follows
Summary
We are first concerned with the study of the nonexistence of global weak solutions to time-fractional evolution inequalities of the form:. In the case where ν = 2, it was shown that under suitable conditions on the initial value u0, if 1 < p ≤ 3, (2)–(4) has no global weak solutions. When ν = 2, it was shown that under suitable conditions for the initial values, if one of the following assumptions is satisfied: (a) N = 2 and 1 < p ≤ k + 1; and (b) N = 2 and p > 1, (2)–(4) has no global weak solutions. The study of the nonexistence of global solutions to time-fractional evolution equations and inequalities has been initiated by Kirane and their collaborators (as can be seen in, e.g., [10,11,12,13,14]).
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