Local Well-Posedness and Blow-Up Phenomena at High Energy Level for Viscoelastic Petrovsky Equations with Logarithmic Nonlinearity
This paper focuses on the blow-up properties of solutions to initial boundary value problem for viscoelastic Petrovsky equations with logarithmic nonlinearity.By employing Faedo-Galerkin approximation technique along with contraction mapping principle,the local well-posedness of the problem is established.Moreover,combining contradiction argument and concavity lemma,we prove that the solution blows up in finite time at high energy level.
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