Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Chen, H.; Jiang, Jingfei; Cao, Dengqing; Fan, Xiaoming

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Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

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03. Okt. 2018

Applied Mathematics and Nonlinear Sciences

Band 3 (2018): Heft 1 (Juni 2018)

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Online veröffentlicht: 03. Okt. 2018

Seitenbereich: 175 - 186

Eingereicht: 09. März 2018

Akzeptiert: 17. Mai 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00014

Schlüsselwörter
nonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent

© 2018 H. Chen et al., published by Sciendo.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Supports of invariant measure and random attractors for φNGM3 with case I

Section of global random basic attractors for φNGM3 with case II

Section of global random point attractors for φNGM3 with case II

Section of global random attractors for φNGM3 with case II

Section of global point/basic attractors for S(τ,τ–t,ω) with case II

Section of global random basic attractors for φNGM3 with case III

Section of global random point attractors for φNGM3 with case III

Section of boundary of global random attractors for φNGM3 with case III

Section of global random basic attractors for φNGM3 with case IV

Section of global random point attractors for φNGM3 with case IV

Section of boundary of global random attractors for φNGM3 with case IV

The values of α and corresponding Hasudorff dimension

	Case I	Case II	Case III	Case IV
α	1	2.4	4	6

Hausdorff dimenison	0	1	2	3

The one to for order eigenvalues for A

λ₁	λ₂	λ₃	λ₄
1.0270	4.1081	9.2431	16.4329

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Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Online veröffentlicht: 03. Okt. 2018

Seitenbereich: 175 - 186

Eingereicht: 09. März 2018

Akzeptiert: 17. Mai 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00014

Schlüsselwörter
nonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent

© 2018 H. Chen et al., published by Sciendo.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

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Fig. 5

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Fig. 11

The values of α and corresponding Hasudorff dimension

The one to for order eigenvalues for A

Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

H. Chen

Jingfei Jiang

Dengqing Cao

Xiaoming Fan

Online veröffentlicht: 03. Okt. 2018

Seitenbereich: 175 - 186

Eingereicht: 09. März 2018

Akzeptiert: 17. Mai 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00014

Schlüsselwörternonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent

© 2018 H. Chen et al., published by Sciendo.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

The values of α and corresponding Hasudorff dimension

The one to for order eigenvalues for A

Schlüsselwörter
nonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent