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In this paper, we split the 3-D linearly elastic shell problem into a 2-D problem by using the approach of formal asymptotic expansion. The approximate solution UKT(x, ξ) for the 3-D linearly elastic shell consists of [image omitted] , where u0, u1, u2 are independent of ξ. The leading term u0 satisfies a 2-D elliptic boundary value problem, and other terms u1, u2 will be derived using the algebraic expression for u0 without solving PDEs. We prove that the solution u0(x) exists and is unique, and give the error estimation for an elliptic membrane, which is smaller than the error with other models. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of two cubic quasi–linear Klein–Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non–resonance assumption to that under the resonance assumption. [ABSTRACT FROM AUTHOR]

Let , be a formal power series solution of a nonlinear partial differential equation. We study multisummability of . This paper is a continuation of [S. Ōuchi, Multisummability of formal solutions of some linear partial differential equations, J. Differential Equations 185 (2002), 513–549], where linear partial differential equations were treated. [ABSTRACT FROM AUTHOR]

In [`Robin function and conformal welding - A new proof of the existence', submitted] a new proof of the existence of the Robin function is given using conformal welding. This proof is essentially based on the simply connected case and a conformal mapping which maps the domain onto a complement of a disk and a system of radial spires. The aim of this note is to show that this proof also has a wider meaning, namely that this mapping is the unique solution of extremal problems, which minimizes the length or the diameter of a subset of the boundary curve. As a consequence we obtain sharp inequalities for the Robin capacity and the logarithmic capacity. [ABSTRACT FROM AUTHOR]