This paper demonstrates the existence of weak solutions for pseudo-parabolic equations, implying significant qualitative properties in mathematical models.
In this paper, we study the Cauchy problem for pseudo-parabolic equations with a logarithmic nonlinearity. After establishing the existence and uniqueness of weak solutions within a suitable functional framework, we investigate several qualitative properties, including the asymptotic behaviour and blow-up of solutions as t→ +∞ . Moreover, when the initial data are close to a Gaussian function, we prove that these weak solutions exhibit either super-exponential growth or super-exponential decay.
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Alves et al. (2025) studied this question.
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