Naofumi Honda

Virtual turning points

The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painleve equations of the Noumi Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary

Conditional stability for a single interior measurement

An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have complex coefficients in a bounded domain with C2 boundary. We are given a single interior measurement. This means that we know a given solution of the forward equation in this domain. The equation includes some model equations arising from acoustics, viscoelasticity and hydrology. We assume that the coefficients are piecewise analytic. Our major result is the local Holder stability estimate for identifying the unknown coefficients. If the unknown coefficient is a complex coefficient in the principal part of the equation, we assumed a condition which we name admissibility assumption for the real part and imaginary part of the difference of two complex coefficients. This admissibility assumption is automatically satisfied if the complex coefficients are real valued. For identifying either the real coefficient in the principal part or the coefficient of the 0th order of the equation, the major result implies global uniqueness for the identification.

Uniqueness in the Inverse Boundary Value Problem for Piecewise Homogeneous Anisotropic Elasticity

Consider a three dimensional piecewise homogeneous anisotropic elastic medium

On the Algebraic Study of Asymptotics

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Foundation of symbol theory for analytic pseudodifferential operators, I

which is a bounded domain consisting of a finite number of bounded subdomains

Application to the Noumi-Yamada System with a Large Parameter

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Definition and Basic Properties of Virtual Turning Points

, with each

Exact WKB Analysis of Non-adiabatic Transition Problems for 3-Levels

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Regular sequences associated with the Noumi-Yamada equations with a large parameter

a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an anisotropic elastic medium. Assuming the

Virtual turning points — A gift of microlocal analysis to the exact WKB analysis

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