Abstract. We study positive blowing-up solutions of the system:as well as of some more general systems. For any p, q > 1, we prove single-point blow-up for any radially decreasing, positive and classical solution in a ball. This improves on previously known results in 3 directions:(i) no type I blow-up assumption is made (and it is known that this property may fail);(ii) no equidiffusivity is assumed, i.e. any δ > 0 is allowed; (iii) a large class of nonlinearities F (u, v), G(u, v) can be handled, which need not follow a precise power behavior.As side result, we also obtain lower pointwise estimates for the final blow-up profiles.

Abstract. In this paper, we consider positive solutions of the systemand p, q, r, s > 1 . We prove single-point blow-up if r < q + 1 and s < p + 1 and for a large class of radial decreasing solutions. This extends the result of Friedman and Giga for this basic system known only for p = q = r = s . We also obtain lower pointwise estimates for the blow-up profiles.Mathematics subject classification (2010): 35B20, 35B40, 35B50, 35K55, 35K57, 35K58.

In this work, we prove single-point blow-up for any positive, radially decreasing, classical and blowing-up solution of a system of m ≥ 3 heat equations in a ball of R n , which are coupled cyclically by superlinear monomial reaction terms. We also obtain lower pointwise estimates for the blow-up profiles.

This paper is concerned with nonnegative solutions of the reaction-diffusion system:In a suitable range of parameters, we prove (initial and final) blow-up rates, as well as universal bounds for global solutions. This is done in connection with new Liouville-type theorems in a half-space, that we establish. Primary 35B44; secondary 35K57; 35K58 MSC:

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