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The Time Asymptotic Expansion of the Bipolar Hydrodynamic Model for Semiconductors
In 2003, Gasser-Hsiao-Li [JDE (2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors (HD model) without do**...
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Asymptotic expansion of an estimator for the Hurst coefficient
Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. We first derive the expansion formula of...
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Asymptotic Expansion of the Solutions to a Regularized Boussinesq System (Theory and Numerics)
We consider the propagation of surface water waves described by the Boussinesq system. Following (Molinet et al. in Nonlinearity 34:744–775,
2021 ),...
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Asymptotic Behavior of Solutions of the Nonstationary Schrödinger Equation with Potential that Slowly Depends on Time
We study the asymptotic behavior of solutions of the Cauchy problem for the nonstationary Schrödinger equation with a potential that slowly depends...
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Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus
This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential...
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On Some Asymptotic Expansions of Skew Diffusions
Relying on a perturbation technique of Markov semigroup, also known as the parametrix method, we establish some asymptotic expansion for the Markov...
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Asymptotic Expansion at Infinity of Solutions of Special Lagrangian Equations
We obtain a quantitative high-order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine...
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Time-Periodic Case
Chapter Time-Periodic Case is devoted to the time-periodic setting of the Navier–Stokes problem in thin structures. The existence and uniqueness of a...
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Large-Time Asymptotic Behaviors for Linear Blackstock’s Model of Thermoviscous Flow
In the classical theory of acoustic waves, Blackstock’s model was proposed in 1963 to characterize the propagation of sound in thermoviscous fluids....
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Asymptotic Expansions
One of the techniques used in the latest case study (Section 3.7 ) is an asymptotic expansion of an...
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Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations
In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and...
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Asymptotic Behavior
In this chapter we show that all lower and upper Lyapunov exponents, both to the future and to the past, belong to some connected component of the...
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Second-Order Three-Scale Asymptotic Analysis and Algorithms for Steklov Eigenvalue Problems in Composite Domain with Hierarchical Cavities
A top–down strategy based on the second-order asymptotic method is proposed for solving the Steklov eigenvalue problems on composite perforated...
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On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schrödinger Operator
AbstractThe one-dimensional Schrödinger operator with potential growing at infinity and with a semiclassical small parameter is considered. We...
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Witten deformation on non-compact manifolds: heat kernel expansion and local index theorem
Asymptotic expansions of heat kernels and heat traces of Schrödinger operators on non-compact spaces are rarely explored, and even for cases as...
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Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer
The paper deals with Markovian multiserver retrial queuing system with exponential abandonments, two types of arrivals: Fresh calls and Handover...
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator
In this paper, we apply the steepest descent method to the Schläfli-type integral representation of the three-parameter Mittag-Leffler function...
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Asymptotic Justification of Equations for von Kármán Membrane Shells
AbstractThe objective of this work is to study the asymptotic justification of the two- dimensional equations for membrane shells with boundary...
