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Authors: ABITA RAHMOUNE, BENABDERRAHMANE BENYATTOU.
DOI: 10.24193/subbmath. 2021.3.11
Published Online: 2021-09-30
Published Print: 2021-09-30
pp. 553-566
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This research considers a class of quasi-linear parabolic equation with variable exponents:
a(x,t)ut−Δm (.)u=f(u),
in which fp(.)(u) the source term, a (x,t)>0 is a nonnegative function and the exponents of nonlinearity m(x), p(x) are given measurable functions. Under suitable conditions on the given data a finite-time blow-up result of solutions is proven if the initial datum possesses suitable positive energy and in this case, we precise estimate for the lifespan T*of the solution. A blow-up of the solutions with negative initial energy is also established.
Mathematics Subject Classification (2010): 35K92, 35B44, 35A01.
Keywords: Global nonexistence, quasi-linear evolution equation, Sobolev spaces with variable exponents, variable nonlinearity.
