Asymptotic Analysis - Volume 85, issue 3-4

Authors: Li, Yachun | Peng, Yue-Jun | Wang, Ya-Guang

Article Type: Research Article

Abstract: We consider quasi-neutral limits in two-fluid isentropic Euler–Poisson equations arising in the modeling of unmagnetized plasmas and semiconductors. For periodic smooth solutions, we justify an asymptotic expansion in a time interval independent of the Debye length. This implies the convergence of the equations to compressible Euler equations. The proof is based on energy estimates for symmetrizable hyperbolic equations and on the exploration of the coupling between the Euler equations and the Poisson equation.

Keywords: two-fluid Euler–Poisson system, the quasi-neutral limit, compressible Euler equations, local smooth solutions

DOI: 10.3233/ASY-131177

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 125-148, 2013

Authors: Pham, Phuong Nguyen

Article Type: Research Article

Abstract: In this article, we prove the existence of weak solutions of variational parabolic inequalities with pseudo-monotonicity and nonzero initial data using finite differences in time.

Keywords: nonlinear pseudo-monotonicity, existence, weak solution, parabolic variational inequality, finite differences in time

DOI: 10.3233/ASY-131178

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 149-165, 2013

Authors: Sánchez, Justino | Vergara, Vicente

Article Type: Research Article

Abstract: We study the long-time behavior of bounded solutions of certain systems of nonlinear integro-differential equations, including differential equations of fractional order between 1 and 2. We obtain appropriate Lyapunov functions for this system and prove that any bounded global solution converges to a steady state if the nonlinear potential E occurring in the system satisfies the Łojasiewicz inequality.

Keywords: integro-differential equations, fractional derivative, gradient system, Lyapunov function, convergence to steady state, Łojasiewicz inequality

DOI: 10.3233/ASY-131180

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 167-178, 2013

Authors: Trostorff, Sascha

Article Type: Research Article

Abstract: We give an approach to exponential stability within the framework of evolutionary equations due to Picard [Math. Methods Appl. Sci. 32(14) (2009), 1768–1803]. We derive sufficient conditions for exponential stability in terms of the material law operator which is defined via an analytic and bounded operator-valued function and give an estimate for the expected decay rate. The results are illustrated by three examples: differential-algebraic equations, partial differential equations with finite delay and parabolic integro-differential equations.

Keywords: exponential stability, evolutionary equations, causality, differential-algebraic equations, delay-equations, integro-differential equations

DOI: 10.3233/ASY-131181

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 179-197, 2013

Authors: Chipot, Michel | Roy, Prosenjit | Shafrir, Itai

Article Type: Research Article

Abstract: We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem and show in particular, that in general the limiting behavior is very different from the one for the Dirichlet boundary conditions.

Keywords: eigenvalue problem, ℓ goes to plus infinity, dimension reduction

DOI: 10.3233/ASY-131182

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 199-227, 2013

Authors: Amour, L. | Khodja, M. | Nourrigat, J.

Article Type: Research Article

Abstract: In this paper, we derive a semiclassical asymptotic expansion of the Wick symbol, for the product of two operators, when the first one is a Weyl pseudodifferential operator in the class of Calderón–Vaillancourt and the second one is trace class in L2 (Rn ). This result is extended in the direction of Schatten classes. We also report a corresponding result in the context of anti-Wick operators. The Wick expansion is used to derive an equation satisfied, up to an arbitrary small error term, by the Wick symbol of density operators governed by the time dependent Hartree–Fock (TDHF) equation. Still in …the situation of the TDHF dynamics, we prove the finiteness of the Ehrenfest time. Show more

Keywords: Wick calculus, anti-Wick quantization, semiclassical analysis, Schatten classes, time dependent Hartree–Fock, Ehrenfest time

DOI: 10.3233/ASY-131184

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 229-248, 2013

Article Type: Other

Citation: Asymptotic Analysis, vol. 85, no. 3-4, pp. 249-250, 2013