Results 41 to 50 of about 5,198,351 (376)
Embedding of global attractors and their dynamics [PDF]
Proceedings of the American Mathematical Society, 2011 Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ordinary differential equation in ${\mathbb R}^{m+1}$, with $m >d$, that has unique solutions and ...
Pinto de Moura, Eleonora +2 more
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Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity
International Journal of Mathematics and Mathematical Sciences, 2011 We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial condition u(x,0)=u0(x). We prove existence of a global attractor in space H2(Ω), by using decomposition method with cut-off function and ...
Zai-yun Zhang, Zhen-hai Liu
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iScience, 2020 Summary: Cancer metabolism is critical for understanding the mechanism of tumorigenesis, yet the understanding is still challenging. We studied gene-metabolism regulatory interactions and quantified the global driving forces for cancer-metabolism ...
Wenbo Li, Jin Wang
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Statistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations
AIMS Mathematics, 2022 This article studies the discrete Zakharov equations with impulsive effect. The authors first prove that the problem is global well-posed and that the process formed by the solution operators possesses a pullback attractor. Then they establish that there
Binbin Miao, Chongbin Xu, Caidi Zhao
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Direct transition to high-dimensional chaos through a global bifurcation [PDF]
, 2005 In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step.
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The finite dimensional global attractor for the 3D viscous Primitive Equations
, 2016 A new method is presented to prove finiteness of the fractal and Hausdorff dimensions of the global attractor for the strong solutions to the 3D Primitive Equations (PEs) with viscosity, which is applicable to more general situations than the ...
N. Ju
semanticscholar +1 more source
Global attractor for a strongly damped wave equation with fully supercritical nonlinearities
, 2016 The paper investigates the existence of global attractor for a strongly damped wave equation with fully supercritical nonlinearities: \begin{document}$ u_{tt}-Δ u- Δu_t+h(u_t)+g(u)=f(x) $\end{document} .
Zhijian Yang, Zhiming Liu
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Existence and attractors of solutions for nonlinear parabolic systems
Electronic Journal of Qualitative Theory of Differential Equations, 2001 We prove existence and asymptotic behaviour results for weak solutions of a mixed problem (S). We also obtain the existence of the global attractor and the regularity for this attractor in $\left[H^{2}(\Omega )\right] ^{2}$ and we derive estimates of its
Hamid El Ouardi, Abderrahmane El Hachimi
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Mathematical Biosciences and Engineering, 2020 In this paper we introduce a method of global exponential attractor in the reaction-diffusion epidemic model in spatial heterogeneous environment to study the spread trend and long-term dynamic behavior of the COVID-19 epidemic.
Cheng-Cheng Zhu, Jiang Zhu
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Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction
, 2017 In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension, the existence ...
Iuorio, Annalisa, Melchionna, Stefano
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