Blow-up in finite time for a pseudo-parabolic equation with variable exponents

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This paper investigates the blow-up phenomenon in a class of pseudo-parabolic equations with variable exponents. We demonstrate that the solutions to the corresponding initial boundary value problem blow up in finite time when the initial energy is positive and the initial data is sufficiently large. Recently, a blow-up result for this equation with non-positive initial energy was established in Applied Mathematics Letters (2023). Notably, we have eliminated the conditions typically imposed by Sobolev's inequality, this process is applicable to a variety of equations.