Asymptotic Analysis - Volume 12, issue 2

Authors: Novokshenov, V.Yu.

Article Type: Research Article

Abstract: The large-time asymptotic solution of the Sine-Gordon equation is considered describing the decay of a step-like initial condition with nonidentical finite-gap limits as x→±∞. The leading term of asymptotics is found as a finite-gap quasi periodic solution with its phase vectors modulated by a slow space-like variable. The Whitham equations describing the modulation are studied in detail for the case of complex-valued group velocities, which arise for the problem above. The existence and uniqueness theorems for these equations are proved and a complete picture of the. Whitham deformation is given for the case of a periodic one-gap boundary condition at …the left infinity and zero at the right infinity. Show more

DOI: 10.3233/ASY-1996-12201

Citation: Asymptotic Analysis, vol. 12, no. 2, pp. 77-89, 1996

Authors: Stolovitch, Laurent

Article Type: Research Article

Abstract: Nous étudions les champs de vecteurs analytiques X de (Cn ,0) à partie linéaire diagonale non-nulle et dont les valeurs propres λi satisfont d'une part à des relations de résonnance toutes engendrées par une seule relation r1 λ1 +…+rn λn =0 avec des ri ∈N non tous nuls, et d'autre part à une condition de petits diviseurs diophantiens. Nous montrons que lorsque x1 r1 …xn rn n'est pas une intégrale première d'une forme normale de X, alors X admet une forme normale polynômiale. Si cette dernière vérifie certaines hypothèses, nous obtenons une classification analytique des champs …formellement équivalents à cette forme normale. Dans le cas particulier de la dimension 2, nous retrouverons les classifications de Martinet-Ramis sans distinguer le cas d'une valeur propre nulle du cas où le rapport des valeurs propres est un rationnel négatif. Show more

DOI: 10.3233/ASY-1996-12202

Citation: Asymptotic Analysis, vol. 12, no. 2, pp. 91-143, 1996

Authors: Fuchs, Martin

Article Type: Research Article

Abstract: We prove local Lipschitz regularity for minimizers of functionals with integrand of polynomial growth near infinity. In contrast to Giaquinta and Modica (see [4]) we do not impose any differentiability or convexity conditions on the data.

DOI: 10.3233/ASY-1996-12203

Citation: Asymptotic Analysis, vol. 12, no. 2, pp. 145-151, 1996

Authors: Colin, T.

Article Type: Research Article

Abstract: We consider a simplified model of ocean circulation. We give a mathematical justification of a singular limit process which leads to the Sverdrup relation. This singular limit implies the existence of boundary layers that correspond to currents intensification near the western coast of oceans.

DOI: 10.3233/ASY-1996-12204

Citation: Asymptotic Analysis, vol. 12, no. 2, pp. 153-168, 1996