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A Quasilinear Hierarchical Size-Structured Model: Well-Posedness and Approximation
A finite difference approximation to a hierarchical size-structured model with nonlinear growth, mortality and reproduction rates is...
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Local Existence of the Shock Front Solution to the Axi–symmetrical Piston Problem in Compressible Flow
In this paper, we study a kind of 2–dimensional axi–symmetrical piston problem in compressible flow. The corresponding mathematical model is the...
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Analysis of an Age Structured SEIRS Epidemic Model with Varying Total Population Size and Vaccination
This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at...
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Asymptotic Limits in Macroscopic Plasma Models
A model hierarchy of macroscopic equations for plasmas consisting of electrons and ions is presented. The model equations are derived from the...
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Hypersurfaces with Flat Centroaffine Metric and Equations of Associativity
It is demonstrated that hypersurfaces M n ⊂ A n +1 with a flat centroaffine metric are governed by a system of nonlinear PDEs known as the equations of...
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Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval
This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws u ...
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On the Cauchy Problem for the Equations of Ideal Compressible MHD Fluids with Radiation
We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects....
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Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms
In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of...
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Emerging Patterns in a Hyperbolic Model for Locally Interacting Cell Systems
Morphogenetic processes such as neurulation and gastrulation involve co- ordinated movements of cells. It is assumed that these processes happen due...
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An initial boundary value problem in ideal Magneto-Hydrodynamics
We consider the initial-boundary value problem for the system of equations of ideal Magneto-Hydrodynamics with a perfectly conducting wall boundary...
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Transport and instability for perfect fluids
Incompressible perfect fluids are described by the Euler equations. We provide a new simple proof for well-posedness for velocities in
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The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an...
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A One-Dimensional Fluid Dynamic Model of the Systemic Arteries
The systemic arteries are modeled as a bifurcating tree of compliant and tapering vessels. Blood flow and pressure in the vessels are determined by...
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Nonexistence results of solutions of semilinear differential inequalities on the Heisenberg group
Denoting Δ ? the Laplacian operator on the (2 N +1)-dimensional Heisenberg group ? N , we prove some nonexistence results for solutions of inequalities...
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Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D
Systems of nonlinear hyperbolic conservation laws in two space dimensions are considered which are characterized by the fact that the coupling of...