Advances in Differential Equations and Control Processes
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Abstract: This paper deals with the blow-up properties of positive
solution to the nonlocal in space and time degenerate parabolic equation
with homogeneous
Dirichlet conditions and nonnegative nontrivial initial datum.Thelocalexistenceanduniquenessoftheclassicalpositivesolution are
established. Under appropriate hypotheses, it is shown that all positive
solutions blow up in finite time. It is also proved that the blow-up set is the
whole domain. And these differfromthelocalsourcecaseandthe case with only space
integral source. Furthermore, the blow-up rate is precisely determined for the
two special cases:and
Keywords and phrases: degenerate parabolic equation, space-time integral source, global existence, global blow-up, asymptotic behavior.
