Attractors for the semilinear reaction–diffusion equation with distribution derivatives in unbounded domains☆

By Chunyou Sun, Chengkui Zhong. 2005

70 citations recorded by the source corpus.

Abstract In this paper, we prove the existence of global attractors for a nonlinear reaction–diffusion equation with a nonlinearity having a polynomial growth of arbitrary order p - 1 ( p ⩾ 2 ) , and with distribution derivatives in the inhomogeneous term. The global attractors are obtained in L 2 ( R n ) and L p ( R n ) , respectively. A new a priori estimate method has been used. Since the solutions of the equation have no higher regularity and the semigroup associated with the solutions is not continuous in L p ( R n ) , the results are new and appear to be optimal.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d762bf8521c46470c731f9a26cf849ca8b80b698

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In Applied Mathematics

1. Bixiang Wang
2. Yuncheng You
3. Chunyou Sun
4. Sufang Wang
5. Chengkui Zhong
6. Yangrong Li

In Computational Theory and Mathematics

1. Bixiang Wang
2. Yuncheng You
3. Chunyou Sun
4. Sufang Wang
5. Chengkui Zhong
6. Shengfan Zhou
7. Yangrong Li
8. Anhui Gu

In Control and Systems Engineering

1. Bixiang Wang
2. Yuncheng You
3. Chunyou Sun
4. Sufang Wang
5. Chengkui Zhong
6. Shengfan Zhou
7. Yangrong Li
8. Kening Lu

Citations in the corpus

• Global Attractors for a Nonclassical Diffusion Equation (2007, methodology): “And how to prove the existence of the (H 1 0 (Ω) ,L p (Ω))-global attractor? Our method (or precisely, the byproduct) gives a general method for proving the existence of the (H 1 0 (Ω) ,L p (Ω))-global attractor (see [ 12 ] for the cases of reaction-diffusion equations in unbounded domains).”
• Global Dynamics of the Brusselator Equations (2007, methodology): “The spectral decomposition [17] and the spatial cut-off decomposition [28] were also introduced to address the existence of global attractors for certain classes of scalar nonlinear reaction-diffusion equations in L spaces, or on unbounded domains.”
• 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.”
• 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].”