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Solutions of the Camassa-Holm Equation Near the Soliton
In this paper, solutions of the Camassa-Holm equation near the soliton Q is decomposed by pseudo-conformal transformation as follows: λ 1/2 ( t ) u ( t, λ ( t )
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Stability of the rarefaction wave in the singular limit of a sharp interface problem for the compressible Navier-Stokes/Allen-Cahn system
This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface...
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Application of Resurgent Analysis to the Construction of Asymptotics of Linear Differential Equations with Degeneration in Coefficients
This paper is a review of results concerning the construction of asymptotics of solutions to degenerate linear differential equations with...
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Dynamic Analysis of the Multi-state Reliability System with Priority Repair Discipline
This paper considers a multi-state repairable system that is composed of two classes of components, one of which has a priority for repair. First, we...
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Navier-Stokes/Allen-Cahn System with Generalized Navier Boundary Condition
In this paper, we focus on the immiscible compressible two-phase ow described by the coupled compressible Navier-Stokes system and the modi ed...
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Asymptotic Equations of Gas Dynamics: Qualitative Analysis, Construction of Solutions, and Applications
In this paper, we propose asymptotic expansions for the velocity potential and obtain asymptotic equations of gas dynamics for irrotational...
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Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System
This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of...
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A Global Existence Result for Korteweg System in the Critical LP Framework
The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin...
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Estimates of Initial Scales for Layers with Small Random Negative-Definite Perturbations
In this work, we consider the Schrödinger operator in a multi-dimensional layer with small random perturbations. Perturbations are distributed in...
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On Parametric Gevrey Asymptotics for Some Initial Value Problems in Two Asymmetric Complex Time Variables
We study a family of nonlinear initial value problem for partial differential equations in the complex domain under the action of two asymmetric time...
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High Frequency Oscillations of First Eigenmodes in Axisymmetric Shells as the Thickness Tends to Zero
The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2ε) tends...
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Asymptotic expansions for solutions of parabolic systems associated with multi-scale switching diffusions
This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching...
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Higher-order crack tip fields for functionally graded material plate with transverse shear deformation
The crack tip fields are investigated for a cracked functionally graded material (FGM) plate by Reissner’s linear plate theory with the consideration...
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Asymptotics of a solution to the time-periodic heat equation set in domains with corner points
We study a time-periodic heat equation in a domain with a corner point. Using the Fourier transform and the theory of elliptic problems set in...
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Converging Expansions for Lipschitz Self-Similar Perforations of a Plane Sector
In contrast with the well-known methods of matching asymptotics and multiscale (or compound) asymptotics, the “functional analytic approach” of Lanza...
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Strongly Regular Multi-level Solutions of Singularly Perturbed Linear Partial Differential Equations
We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain....