## Pullback $$\mathcal{D}$$-attractor of nonautonomous three-component reversible Gray-Scott system on unbounded domains.(English)Zbl 1470.35182

Summary: The long time behavior of solutions of the nonautonomous three-components reversible Gray-Scott system defined on the entire space $$\mathbb{R}^n$$ is studied when the external forcing terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in $$\left[L^2 \left(\mathbb{R}^n\right)\right]^3$$ and $$\left[H^1 \left(\mathbb{R}^n\right)\right]^3$$, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.

### MSC:

 35K51 Initial-boundary value problems for second-order parabolic systems 35B41 Attractors 35B45 A priori estimates in context of PDEs 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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### References:

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