Attractors for reaction-diffusion equations in R N with continuous nonlinearity

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Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains (2008, methodology): “The tail-estimates approach was developed in [41] for deterministic PDEs and used in [1, 2, 4, 30, 33, 35, 38, 39].”
Random Attractors for the Stochastic FitzHugh-Nagumo System on Unbounded Domains (2008, methodology): “Under certain circumstances, the tail-estimates method must be used to deal with the problem caused by the unboundedness of domains.”
On the connectedness and asymptotic behaviour of solutions of reaction–diffusion systems☆ (2006, background): “The case of reaction–diffusion systems in unbounded domains is considered in [27].”
Random attractors for stochastic reaction–diffusion equations on unbounded domains (2009, background): “Then, following [24], one may take the domain to be a sequence of balls with radius approaching ∞ to deduce the existence of a weak solution to (3.”