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Let $S (λ)$ be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle $𝒪 \subset R^{n}$ , $n \geq 3$ with Dirichlet or Neumann boundary conditions on $\partial 𝒪$ . The function $s (λ)$ , called scattering phase, is determined from the equality $e^{- 2 π i s (λ)} = \det S (λ)$ . We show that $s (λ)$ has an asymptotic expansion $s (λ) \sim \sum_{j = 0}^{\infty} c_{j} λ^{n - j}$ as $λ \to + \infty$ and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.

Asymptotic Energy Propagation and Scattering of Waves in Waveguides with Cylinders.

William C. Lydord (1976)

Mathematische Annalen

Asymptotic expansions for linear symmetric hyperbolic systems with small parameter.

Hawamdeh, O., Perjan, A. (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic solutions of equations with slowly varying coefficients

V. P. Maslov (1989/1990)

Séminaire Équations aux dérivées partielles (Polytechnique)

Asymptotic stability for a nonlinear evolution equation

Zhang Hongwei, Chen Guowang (2004)

Commentationes Mathematicae Universitatis Carolinae

We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation $(| u_{t} {|^{r - 2} u_{t})}_{t} - Δ u_{t t} - Δ u - δ Δ u_{t} = f (u)$ .

Asymptotic theory for weakly nonlinear wave equations in semi-infinite domains.

Easwaran, Chirakkal V. (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic time-behavior for weighted scalar conservation laws

Philippe Le Floch, J. C. Nedelec (1988)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Asymptotic wave functions and energy distribution in magnetodynamics.

Geraldo S.S. Avila (1987)

Journal für die reine und angewandte Mathematik

Asymptotically periodic solutions for a class of nonlinear coupled oscillators.

Cazenave, Thierry, Weissler, Fred B. (1995)

Portugaliae Mathematica

Asymptotics for conservation laws involving Lévy diffusion generators

Piotr Biler, Grzegorz Karch, Wojbor A. Woyczyński (2001)

Studia Mathematica

Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their $L^{p}$ -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.

Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results

B. Baji, A. Cabot, J. I. Díaz (2007)

Annales de l'I.H.P. Analyse non linéaire

Behavior of critical solutions of a nonlocal hyperbolic problem in Ohmic heating of foods.

Kavallaris, Nikos I., Tzanetis, Dimitrios E. (2002)

Applied Mathematics E-Notes [electronic only]

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