Abstract
In this work, we are concerned with a nonlinear wave equation with variable exponents. In the presence of the logarithmic nonlinear source, we established a global nonexistence result with negative initial data and without imposing the Sobolev Logarithmic Inequality. The blow-up time is established with upper bound and lower bound. In addition, under some conditions on the initial data and for a specific class of relaxation functions, we established an infinite time blow-up result.
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