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.