Qualitative methods reveal global existence and blow-up of weak solutions for nonlinear equations, indicating crucial behavior.
In this paper, we consider a nonlinear parabolic m(x)-biharmonic equation with logarithmic source terms. Applying the potential well method combined with the Nehari manifold, the global existence and blow-up of weak solutions is proved. In addition, we establish decay estimates for the global weak solutions.
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Butakın et al. (2025) studied this question.
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