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Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

100%

Jia X., Gao J., Ding X.

Open Mathematics

2016

tom 14

nr 1

586-602

In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

64%

Bárta T.

Open Mathematics

2013

tom 11

nr 6

1112-1128

We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.

Ograniczanie wyników

2 Open Mathematics

1 Bárta T.

1 Ding X.

1 Gao J.

1 Jia X.

1 2016

1 2013

Wyniki wyszukiwania

Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids