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Finite-time blow-up and global convergence of solutions to a nonlocal parabolic equation with conserved spatial integral. (English) Zbl 1379.35040

Summary: In this note we investigate the evolution behaviour of the solutions to a nonlocal parabolic equation with conserved spatial integral. For the non-global solutions, the blow-up rate for \(L^p\) norm of the solutions is estimated from below. For several classes of initial data, the convergence of the global solutions is established.

MSC:

35B44 Blow-up in context of PDEs
35R09 Integro-partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
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