The University of Tokyo · Mathematics
Professor Masahiro Yamamoto's research lab specializes in mathematical analysis of inverse problems, particularly in the context of partial differential equations (PDEs) and their applications in engineering and physics. The lab focuses on developing theoretical and numerical methods for solving ill-posed problems, including coefficient identification in parabolic and hyperbolic equations, Cauchy problems for elliptic equations, and stability analysis using Carleman estimates and regularization techniques. A central theme is the application of advanced analytical tools—such as boundary control theory, Volterra integral equations, and Tikhonov regularization—to ensure robust and stable reconstructions of unknown parameters or initial conditions from limited observations. The lab also explores the interplay between mathematical modeling and real-world applications in heat transfer, structural health monitoring, and industrial product evaluation.
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methods for applications of the Carleman estimates to estimates of solutions and to inverse problems.
In spite of the fact that product appearance would not seem to bear upon performance, this article provides evidence that the appearance of an industrial product may have an impact on its evaluation. Utilizing a conjoint scaling approach, Mel Yamamoto and David R. Lambert find that industrial product appearance exerts an influence, which in some circumstances exceeds the influence of certain product performance or price attributes. They suggest that attention paid to product aesthetics may have
Let u ( f ) be the solution to a hyperbolic equation in a bounded domain s2 c B ' :and r c~ iJs2 is given.We consider an inverse problem of dete-ingFor a sufficiently large T > 0, we will show the stability estimate of IlfllLqn, by Ilau(f)/anllH,c,,,T:'~tn,. areconstruction formulaof f f" au(f)/an and a Tikhoaov regularization.Our methodology is based on exact boundary cnntrollability and a Voltem integral equation of the first kind with kernel U .
Given the measurement of temperature at a fixed time θ>0 and the measurement of temperature in a subregion of the physical domain, we investigate the simultaneous reconstruction of the initial temperature and heat radiative coefficient in a heat conductive system. The stability of the inverse problem is first established, and then the numerical reconstruction is mainly studied. The reconstruction process is done by Tikhonov regularization with the regularizing terms being the L2-norms of gradien
This paper investigates the numerical computation of a Cauchy problem for Laplace's equation which is a typical ill-posed problem. By using Green's formula, the problem is transformed to a moment problem. For numerical computation of the moment problem, an error estimation and several numerical examples for verification are presented. Necessary and sufficient conditions for the existence of the solution of the Cauchy problems for Laplace's equation in two-dimension are also given.
An inverse problem of determining a zeroth-order coefficient in a one-dimensional fractional diffusion equation of half-order in time is investigated. Under some assumptions on the regularity of the solutions and coefficients, we prove a conditional stability estimate by some additional data. The key is a Carleman estimate, but since we have no Carleman estimates for the fractional diffusion equation, we further take the t-derivative of half-order to obtain the equation where the principal term
We consider a fractional diffusion equation in x ∈ (0, ℓ) where the derivative in time t is of half order in the sense of Caputo and we establish a Carleman estimate. Since the derivatives of non-natural number orders do not satisfy the integration by parts, which is essential for establishing a Carleman estimate, we twice apply the Caputo derivative to convert the original fractional diffusion equation to a system with a usual partial differential operator: . Next we apply the Carleman estimate
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