Blow-up and lifespan of solutions to a nonlocal parabolic equation at arbitrary initial energy level. (English) Zbl 1538.35096
Summary: We consider a nonlocal parabolic equation. By exploiting the boundary condition and the variational structure of the equation, we prove finite time blow-up of the solution for initial data at arbitrary energy level. We also obtain the lifespan of the blow-up solution. The results generalize the former studies on this equation.
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35K57 | Reaction-diffusion equations |
| 35K55 | Nonlinear parabolic equations |
| 35B35 | Stability in context of PDEs |
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