RD-systems with chemotaxis: global existence, boundedness and blow-up of
solutions
Abstract
result shows that the blow-up is equivalent to the blow-up of the
$L^r-$norms of the solutions for $r$ exceeding some critical
value $r_c.$ Under very loose conditions we give the estimation of
$r_c,$ relying on a variant of Gagliardo-Nirenberg inequality, and a
kind of bootstrap method which is very similar to the Alikakos-Moser
iteration procedure.
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