In the present paper, we consider an important problem from the point of view of application in sciences and mechanic, namely, a class of $ p(x) $-Laplacian type parabolic equation with weak-viscoelasticity. Here, we are concerned with global in time non-existence under suitable conditions on the exponents $ q(x) $ and $ p(x) $ with positive initial energy. We show that the weak-memory term is unable to stabilize problem (1.2) under conditions (1.5) and (1.7). Our main interest in this paper arose in the first place in consequence of a query to blow-up phenomenon.
Citation: Ahmed Himadan. Well defined extinction time of solutions for a class of weak-viscoelastic parabolic equation with positive initial energy[J]. AIMS Mathematics, 2021, 6(5): 4331-4344. doi: 10.3934/math.2021257
In the present paper, we consider an important problem from the point of view of application in sciences and mechanic, namely, a class of $ p(x) $-Laplacian type parabolic equation with weak-viscoelasticity. Here, we are concerned with global in time non-existence under suitable conditions on the exponents $ q(x) $ and $ p(x) $ with positive initial energy. We show that the weak-memory term is unable to stabilize problem (1.2) under conditions (1.5) and (1.7). Our main interest in this paper arose in the first place in consequence of a query to blow-up phenomenon.
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Ahmed Himadan. Well defined extinction time of solutions for a class of weak-viscoelastic parabolic equation with positive initial energy[J]. AIMS Mathematics, 2021, 6(5): 4331-4344. doi: 10.3934/math.2021257
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