WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 23, 2024
Global Existence and Finite Time Blow-Up for the Laplacian Equation with Variable Exponent Sources
Authors: , ,
Abstract: In this paper, we study a class of semilinear m(.)-Laplacian equations with variable exponent
sources. By using the potential well method, we discuss this problem at three different initial energy levels.
When the initial energy is sub-critical, we obtain the blow-up result and estimate the lower and upper bounds of
the blow-up time. In the case of critical initial energy, we prove global existence, asymptotic behavior, and
finite-time blow-up and determine the lower bound of the blow-up time. For super-critical initial energy, we
establish the finite-time blow-up and estimate the lower and upper bounds of the blow-up time.
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Keywords: m(.)-Laplacian parabolic equation, blow-up time, bounds of blow-up time, global existence, critical exponents, variable nonlinearity
Pages: 465-483
DOI: 10.37394/23202.2024.23.48