Global existence and blow up of solutions for pseudo-parabolic equation with singular potential. (English) Zbl 1448.35322
Summary: We consider the initial boundary value problem of pseudo-parabolic equation with singular potential. We obtain global existence, asymptotic behavior and blowup of solutions with initial energy \(J( u_0) \leq d\). Moreover, we estimate the upper bound of the blowup time for \(J( u_0) < 0\) and \(0 < J( u_0) < d\) respectively. Finally, we prove the finite time blowup and estimate the upper bound of the blowup time for the high energy level, i.e., \(J( u_0) > 0\).
MSC:
| 35K70 | Ultraparabolic equations, pseudoparabolic equations, etc. |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B44 | Blow-up in context of PDEs |
| 35K67 | Singular parabolic equations |
Keywords:
pseudo-parabolic equation; singular potential; global existence; asymptotic behavior; blow up; blowup timeReferences:
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