Results 11 to 20 of about 6,539 (268)
Advances in Nonlinear Analysis, 2022 This article deals with the degenerate fractional Kirchhoff wave equation with structural damping or strong damping. The well-posedness and the existence of global attractor in the natural energy space by virtue of the Faedo-Galerkin method and energy ...
Yang Wenhua, Zhou Jun
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Strong Global Attractors for 3D Wave Equations with Weakly Damping
Abstract and Applied Analysis, 2012 We consider the existence of the global attractor A1 for the 3D weakly damped wave equation. We prove that A1 is compact in (H2(Ω)∩H01(Ω))×H01(Ω) and attracts all bounded subsets of (H2(Ω)∩H01(Ω))×H01(Ω) with respect to the norm of (H2(Ω)∩H01(Ω))×H01(Ω).
Fengjuan Meng
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Attractors for Nonautonomous Parabolic Equations without Uniqueness
International Journal of Differential Equations, 2010 Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the ...
Cung The Anh, Nguyen Dinh Binh
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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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Regularity of Global Attractor for the Reaction-Diffusion Equation
Abstract and Applied Analysis, 2012 By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which ...
Hong Luo
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Cross-attractor modeling of resting-state functional connectivity in psychiatric disorders
NeuroImage, 2023 Resting-state functional connectivity (RSFC) is altered across various psychiatric disorders. Brain network modeling (BNM) has the potential to reveal the neurobiological underpinnings of such abnormalities by dynamically modeling the structure-function ...
Yinming Sun +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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Global Attractor for Sectorial Evolutionary Equation
Journal of Differential Equations, 1996 Let \(A\) be a sectorial operator with compact resolvent in an appropriate Banach space and consider the evolution equation \(\dot u + Au = F(u)\), \(t > 0\), \(u(0) = u_0\). The authors show that this problem generates a dissipative semigroup whenever an appropriate introductory estimate for solutions is known.
Cholewa, Jan W., Dlotko, Tomasz
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Global attractors for p-Laplacian equation
Journal of Mathematical Analysis and Applications, 2007 The existence of a global attractor for the following \(p\)-Laplacian equation: \[ u_t-\text{div}\bigl(|\nabla u|^{p-2}\nabla u\bigr)+f(u)=g \quad\text{in } \Omega\times\mathbb{R}^+,\tag{1} \] with the Dirichlet boundary condition \[ u |_{\partial\Omega}=0\tag{2} \] and initial condition \[ u(x,0)=u_0(x)\tag{3} \] is proved in \(W_0^{1,p}(\Omega)\) and
Yang, Meihua +2 more
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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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