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Article
Quasi-stability and Upper Semicontinuity for Coupled Wave Equations with Fractional Dam**
This paper deals with the long-time dynamics of a nonlinear system of coupled wave equations with fractional dam** term and subjected to small perturbations of autonomous external forces. Inspired by the wor...
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Article
Existence and Regularity of Pullback Attractors for a Non-autonomous Diffusion Equation with Delay and Nonlocal Diffusion in Time-Dependent Spaces
In this paper, we study the asymptotic behavior of solutions to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space ...
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Article
Local existence of solutions to 2D Prandtl equations in a weighted Sobolev space
In this work, we investigate two-dimensional nonlinear Prandtl equations on the half plane and prove the local existence of solutions by energy methods in an exponential weighted Sobolev space. We use the skil...
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Article
Open AccessUpper Semicontinuity of Trajectory Attractors for 3D Incompressible Navier–Stokes Equation
In this paper, we first establish the existence of a trajectory attractor for the Navier–Stokes–Voight (NSV) equation and then prove upper semicontinuity of trajectory attractors of 3D incompressible Navier–St...
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Article
Open AccessUpper semicontinuity of pullback attractors for a nonautonomous damped wave equation
In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. In particular, under some proper assumptions, we prove that the pullback attractor ...
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Article
Dynamics of 2D Incompressible Non-autonomous Navier–Stokes Equations on Lipschitz-like Domains
This paper concerns the tempered pullback dynamics of 2D incompressible non-autonomous Navier–Stokes equations with a non-homogeneous boundary condition on Lipschitz-like domains. With the presence of a time-d...
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Article
Porous yolk–shell-structured carbon nanospheres for electrochemical energy storage
Yolk–shell-structured nanospheres have attracted potential applications in various fields due to their unique structural properties, which combines the advantages of mesoporous carbon and hollow structure. Her...
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Article
Whole-Exome Sequencing Reveals Novel Genetic Variation for Dilated Cardiomyopathy in Pediatric Chinese Patients
Dilated cardiomyopathy (DCM) is characterized by left or bilateral ventricular dilation and systolic dysfunction without rational conditions, which can lead to progressive heart failure and sudden cardiac deat...
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Article
Search of Somatic Mutations of NKX2-5 and GATA4 Genes in Chinese Patients with Sporadic Congenital Heart Disease
Congenital heart disease (CHD) usually occurs sporadically, with only a minority of cases associated with a known genetic mechanism. Cardiac-specific transcription factors NKX2-5 and GATA4 play key roles in th...
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Article
Global Existence and Asymptotic Behavior of Cylindrically Symmetric Solutions for the 3D Infrarelativistic Model with Radiation
In this paper, we establish the global existence, uniqueness and asymptotic behavior of cylindrically symmetric solutions for the 3D infrarelativistic model with radiation in
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Reference Work Entry In depth
Well-Posedness and Asymptotic Behavior for Compressible Flows in One Dimension
This short survey introduces some results on the global well-posedness and asymptotic behavior of strong (generalized) solutions (including the existence of universal (global) attractors) to the 1D nonstationary ...
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Article
Open AccessUpper semicontinuity of uniform attractors for nonclassical diffusion equations
We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.) ...
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Book
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Chapter
Appendix: Basic Inequalities
In this chapter, we shall collect some basic inequalities which play a very crucial role in classical calculus. These inequalities include the Young inequality, the Hölder inequality, the Minkowski inequality,...
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Chapter
Attractors for Evolutionary Differential Equations
In this chapter, we prove the existence of global (uniform) attractors for some evolutionary differential equations. The chapter includes four sections. In Section 3.1, we shall use Theorems 1.1.2 and 2.1.3 to...
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Chapter
Global Existence and Uniqueness for Abstract Evolutionary Differential Equations
In this chapter, we discuss the global existence and uniqueness for some abstract models and ODEs. The chapter consists of three sections. In Section 5.1, we apply Corollary 1.4.4 to prove the global-in-time e...
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Chapter
Asymptotic Behavior of Solutions for Parabolic and Elliptic Equations
In this chapter, we shall study the asymptotic behavior for parabolic and elliptic equations. This chapter embraces three sections. In Section 7.1, we shall use Theorems 2.1.14 and 2.3.7 to establish the unifo...
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Chapter
Global Existence and Uniqueness for Evolutionary PDEs
In this chapter, we present some results on global existence and uniqueness of solutions to evolutionary PEDs obtained by application of analytic inequalities in Chapters 1
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Chapter
Blow-up of Solutions to Nonlinear Hyperbolic Equations and Hyperbolic-Elliptic Inequalities
In this chapter, we shall consider the blow-up of solutions to some nonlinear hyperbolic equations and hyperbolic-elliptic inequalities. This chapter consists of seven sections. In Section 10.1, we apply Theor...
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Chapter
Asymptotic Behavior of Solutions to Hyperbolic Equations
This chapter mainly studies the asymptotic behavior of solutions to some hyperbolic equations. This chapter includes seven sections. In Section 8.1, we shall use Theorem 2.3.11 to study the decay of solutions ...
