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Langa, José Antonio Obaya, Rafael Sanz Gil, Ana María 2020-07-25T11:27:01Z 2020-07-25T11:27:01Z 2020 Nonlinearity, 2020, vol. 33, n. 9, p. 4277-4309. 0951-7715 http://uvadoc.uva.es/handle/10324/41603 10.1088/1361-6544/ab86ce 4277 9 4309 Forwards attraction properties in scalar non-autonomous linear-dissipative parabolic PDEs. The case of null upper Lyapunov exponent 33 As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product semiflow induced by a family of scalar non-autonomous reaction-diffusion equations which are linear in a neighbourhood of zero and have null upper Lyapunov exponent. Besides, the notion of Li-Yorke chaotic pullback attractor for a process is introduced, and we prove that this chaotic behaviour might occur for almost all the processes. When the problems are additionally sublinear, more cases of forwards attraction are found, which had not been previously considered even in the case of linear-dissipative ODEs. eng info:eu-repo/semantics/openAccess Ecuaciones en derivadas parciales Forwards attraction properties in scalar non-autonomous linear-dissipative parabolic PDEs. The case of null upper Lyapunov exponent info:eu-repo/semantics/article