Global nonexistence and blow-up results for a quasi-linear evolution equation with variable-exponent nonlinearities
DOI:
https://doi.org/10.24193/subbmath.2021.3.11Keywords:
Global nonexistence, quasi-linear evolution equation, Sobolev spaces with variable exponents, variable nonlinearity.Abstract
In this paper, we consider a class of quasi-linear parabolic equations with variable exponents,
a (x, t) ut − ∆m(.)u = fp(.) (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 the solution is shown 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 solution with negative initial energy is also established.
Mathematics Subject Classification (2010): 35K92, 35B44, 35A01.
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