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Article
The continuous dependence of the viscous Boussinesq equations uniformly with respect to the viscosity
This paper focuses on the inviscid limit of the incompressible Boussinesq equations in the same topology as the initial data, and proved that the continuous dependence of the viscous Boussinesq equations unifo...
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Article
Open AccessA Generalized Two-Component Camassa-Holm System with Complex Nonlinear Terms and Waltzing Peakons
In this paper, we deal with the Cauchy problem for a generalized two-component Camassa-Holm system with waltzing peakons and complex higher-order nonlinear terms. By the classical Friedrichs regularization met...
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Article
Open AccessGevrey regularity and analyticity for the modified Camassa–Holm equation
This paper deals with the analyticity and Gevrey regularity for the Cauchy problem of a modified Camassa–Holm (mCH) equation in Sobolev–Gevrey space ...
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Article
Nonuniform dependence of solution to the high-order two-component b-family system
This paper deals with the Cauchy problem of the high-order two-component b-family system. Based on the local well-posedness results and prior estimates, two sequences of solutions whose distance initially goes to...
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Article
Well-posedness and wave breaking for a shallow water wave model with large amplitude
Considered herein is the Cauchy problem of a model for shallow water waves of large amplitude. Using Littlewood–Paley decomposition and transport equation theory, we establish the local well-posedness of the e...
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Article
The local well-posedness in Besov spaces and non-uniform dependence on initial data for the interacting system of Camassa–Holm and Degasperis–Procesi equations
This paper deals with the Cauchy problem for the interacting system of the Camassa–Holm and Degasperis–Procesi equations $$\begin{alig...
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Article
A new generalised two-component Camassa–Holm type system with waltzing peakons and wave breaking
This paper mainly investigate the Cauchy problem for the generalised two-component Camassa–Holm type system, which includes the celebrated Camassa–Holm equation, Degasperis equation, Novikov equation, and the ...
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Article
Continuity and analyticity for a cross-coupled Camassa–Holm equation with waltzing peakons and compacton pairs
In this paper, we mainly study the well-posedness in the sense of Hadamard, non-uniform dependence, Hölder continuity and analyticity of the data-to-solution map for a cross-coupled Camassa–Holm equation with ...
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Article
Open AccessPersistence properties for the Fokas-Olver-Rosenau-Qiao equation in weighted \(L^{p}\) spaces
In this paper, we mainly study persistence properties for a generalized Camassa-Holm equation with cubic nonlinearity, and we prove the persistence properties in weighted spaces of the solution to the equation...
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Article
Open AccessConnecting the oxidation of soot to its redox cycling abilities
Although it is known that soot particles are emitted in large quantities to the atmosphere, our understanding of their environmental effects is limited by our knowledge of how their composition is subsequently...
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Article
Boundedness in a parabolic-parabolic chemotaxis system with nonlinear diffusion
This paper deals with the global existence and boundedness of the solutions for the quasilinear chemotaxis system $$\left\{\begin{arra...
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Article
Well-posedness and blowup phenomena for a cross-coupled Camassa–Holm equation with waltzing peakons and compacton pairs
This paper deals with the Cauchy problem for a cross-coupled Camassa–Holm equation $$m_t=-(vm)_x-mv_x, n_t=-(un)_x-nu_x,$$ ...
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Article
Open AccessLocal well-posedness and persistence properties for a model containing both Camassa-Holm and Novikov equation
This paper deals with the Cauchy problem for a generalized Camassa-Holm equation with high-order nonlinearities,
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Article
Open AccessA few remarks on the generalized Novikov equation
This paper deals with the Cauchy problem for a generalized Novikov equation u t ...
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Article
The Properties of Solutions for a Generalized b-Family Equation with Peakons
This paper deals with the Cauchy problem for a shallow water equation with high-order nonlinearities, y t +u ...
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Article
On the boundedness of solutions to the Lorenz-like family of chaotic systems
This paper deals with a class of three-dimensional autonomous nonlinear systems which have potential applications in secure communications, and investigates the localization problem of compact invariant sets o...
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Article
Quenching for a non-local diffusion equation with a singular absorption term and Neumann boundary condition
This paper deals with the quenching phenomenon for a non-local diffusion equation $$u_t(x,t)=\int\limits_\Omega{J(x-y)(u(y,t)-u(x,t))}...
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Article
Open AccessQuenching for a Reaction-Diffusion System with Coupled Inner Singular Absorption Terms
we devote to investigate the quenching phenomenon for a reaction-diffusion system with coupled singular absorption terms, , ...
