Searcharxiv⌕ Search

arXiv subjects

Masahiro Yamamoto

Publications and source records attributed to Masahiro Yamamoto.

At least 19 recordsLinked to original sources
arXiv2026

Operator approach for time-fractional evolution equations in Banach spaces

Our first main purpose is to establish a framework for initial value problems for time-fractional evolution equation of order $α\in (0,1)$ in Banach space $X$: $$ \pppa (u(t)-a) = Au(t) + F(t), \quad 0<t<T. \eqno{(*)} $$ Here $u: (0,T) \rrrr X$ is an $X$-valued function defined in $(0,T)$, and $a \in X$ is an initial value. The operator $A$ satisfies a decay condition of resolvent which is the same as a generator of analytic semigroup. Based on $X$-valued Laplace transforms, we establish a solution formula yielding the well-posedness for (*). In particular, we can directly treat a case $X=L^p(\OOO)$ over a bounded domain $\OOO$ and a uniform elliptic operator $A$. Our theory is feasibly applicable to other topics such as regularity of solutions, inverse problems and control problems.

math.AP↗
arXiv2026

Uniqueness for an inverse problem of determining order and temporal factor of the source for time-fractional evolution equations

This paper addresses the inverse problem of simultaneously recovering the fractional order $α\in (0,1)\cup (1,2)$ and the time-dependent source factor $p(t)$ in the Cauchy problem for an evolution equation with a general self-adjoint operator $A$ in a Hilbert space $X$. The overdetermination condition is given by the scalar product $( u(t), ψ)_X$ for $0 < t < T$, where $ψ\in D(A)$ is an arbitrary fixed element. Uniqueness of the fractional order $α$ is established independently of the specific form of the elliptic operator $A$ and the source function $p(t)$. Furthermore, uniqueness of the factor $p(t)$ is proved not only under the trivial overdetermination $( u(t), ψ)_X = 0$ for all $t \in (0,T)$, but also when the function $t \mapsto ( u(t), ψ)_X$ possesses sufficient smoothness. The proof relies on a decomposition of the solution near $t=0$ into a least smooth component and a smoother remainder.

math.AP↗
arXiv2026

Integral-equation analysis of transient diffusion-limited currents at disk electrodes: Asymptotic expansion and compact approximation

The transient diffusion-limited current at a disk electrode following a change in interfacial ion concentration induced by a potential step is analyzed with direct relevance to chronoamperometric measurements. The mixed-boundary diffusion problem is formulated in the Laplace domain and reduced to a Fredholm integral equation that directly determines the Faradaic current. The steady-state limit recovers Saito's equation, while a systematic long-time asymptotic expansion quantifies the approach to steady state. A Padé approximant yields a compact analytical expression in the time domain that accurately describes the current over experimentally relevant time ranges. In contrast to existing high-accuracy numerical procedures based on hybrid asymptotic and polynomial approximations, the present formulation provides an explicit and compact analytical representation that facilitates interpretation and practical implementation. The short-time response exhibits Cottrell's equation with edge effects characteristic of disk electrodes. Overall, the framework provides practical tools for analyzing transient currents, extracting diffusion parameters, and assessing the accuracy of widely used analytical approximations in disk-electrode chronoamperometry.

physics.chem-ph↗
arXiv2026

Carleman estimates for backward Cahn-Hilliard-reaction-diffusion problems

We study a backward inverse problem for a coupled Cahn-Hilliard-reaction-diffusion system. Our main result is a Carleman estimate for a fourth-order/second-order parabolic system with cross-diffusion terms, which allows us to derive conditional stability estimates for the reconstruction of past states from a single final-time observation: Hölder stability at positive times and logarithmic stability for the initial datum. We then apply the Carleman estimate to a phase-field tumour growth model coupling the tumour volume fraction with a nutrient concentration. In this setting, we obtain backward uniqueness and quantitative stability for the recovery of early tumour states, improving earlier results based on logarithmic convexity, which only yielded uniqueness under an additional smallness assumption on the chemotaxis coefficient. We also discuss how these results support Lipschitz stability on finite-dimensional admissible sets, which is relevant for ensuring convergence of iterative discretisation algorithms.

math.AP↗
arXiv2026

Inverse source problems with reduced interior data for a coupled reaction-diffusion system

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $Ω$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\inΩ$ and $0<t<T$. In this system, called the Klausmeier-Gray-Scott model, we assume that an unknown source depends only on the spatial variable and appears in the reaction-diffusion equation for $u$. The main subject is the inverse source problem of determining a source term from limited data on $(u,v)$. We establish two kinds of stability estimates by means of Carleman estimates. First, a Carleman estimate with a singular weight yields a Lipschitz stability estimate for the inverse source problem from data consisting of a snapshot $u(\cdot,t_0)$ in $Ω$ and $(u,v)$ in a subdomain $ω$ over a time interval. Second, without assuming boundary data, we prove a Hölder stability estimate in any interior subdomain $Ω_0$ satisfying $\overline{Ω_0}\subsetΩ$. We further study how much the observation data can be reduced while preserving uniqueness and stability in the inverse problem under suitable additional conditions.

math.AP↗
arXiv2025

A Model of Causal Explanation on Neural Networks for Tabular Data

The problem of explaining the results produced by machine learning methods continues to attract attention. Neural network (NN) models, along with gradient boosting machines, are expected to be utilized even in tabular data with high prediction accuracy. This study addresses the related issues of pseudo-correlation, causality, and combinatorial reasons for tabular data in NN predictors. We propose a causal explanation method, CENNET, and a new explanation power index using entropy for the method. CENNET provides causal explanations for predictions by NNs and uses structural causal models (SCMs) effectively combined with the NNs although SCMs are usually not used as predictive models on their own in terms of predictive accuracy. We show that CEN-NET provides such explanations through comparative experiments with existing methods on both synthetic and quasi-real data in classification tasks.

cs.LG↗
arXiv2025

Threshold dynamics in time-delay systems: polynomial $β$-control in a pressing process and connections to blow-up

This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized $β$-control method, which replaces conventional linear velocity control with a polynomial of degree $β\ge 1$. The resulting model is a delay differential equation (DDE), for which we derive basic properties through nondimensionalization and analysis. Numerical experiments suggest the existence of a threshold initial velocity separating overshoot and non-overshoot dynamics, which we formulate as a conjecture. Based on this, we design a control algorithm under velocity constraints and confirm its effectiveness. We also highlight a connection between threshold behavior and finite-time blow-up in DDEs. This study provides a practical control strategy and contributes new insights into threshold dynamics and blow-up phenomena in delay systems.

math.OC↗
arXiv2025

Uniqueness in determining multidimensional domains with unknown initial data

This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a multidimensional set. The non-homogeneous part of the equation is expressed as a function satisfying some specific assumptions near a positive time. We establish uniqueness results by incorporating observations that can be on a part of the boundary or in an interior (small) domain. Through this process, we also derive information about the initial data. The main tools required for the proofs include semigroup theory, unique continuation and time analyticity results

math.AP↗
arXiv2025

Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients

We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an explicit solution formula by the eigenfunction expansion method. In order to deal with the case of time-varying coefficients, we first show the unique existence and regularity of solution to a system of time-fractional ordinary differential equations. Then the unique existence of the weak solution to the time-fractional partial differential equation and improved regularity are derived by using the Galerkin method.

math.AP↗
arXiv2025

Initial boundary value problems for time-fractional evolution equations in Banach spaces

We consider an initial value problem for time-fractional evolution equation in Banach space $X$: $$ \pppa (u(t)-a) = Au(t) + F(t), \quad 0<t<T. \eqno{(*)} $$ Here $u: (0,T) \rrrr X$ is an $X$-valued function defined in $(0,T)$, and $a \in X$ is an initial value. The operator $A$ satisfies a decay condition of resolvent which is common as a generator of analytic semigroup, and in particular, we can treat a case $X=L^p(\OOO)$ over a bounded domain $\OOO$ and a uniform elliptic operator $A$ within our framework. First we construct a solution operator $(a, F) \rrrr u$ by means of $X$-valued Laplace transform, and we establish the well-posedness of (*) in classes such as weak solution and strong solutions. We discuss also mild solutions local in time for semilinear time-fractional evolution equations. Finally we apply the result on the well-posedness to an inverse problem of determining an initial value and we establish the uniqueness for the inverse problem.

math.AP↗
arXiv2024

Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part II: Semilinear equations

In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations contain uniformly elliptic spatial differential operators of the second order and the Caputo type fractional derivative acting in the fractional Sobolev spaces as well as a semilinear term that depends on the spatial variable, the unknown function and its gradient. The boundary conditions are formulated in form of the homogeneous Neumann or Robin conditions. For these problems, we first prove uniqueness and existence of their solutions. Under some suitable conditions, we then show the non-negativity of the solutions and derive several comparison principles. We also apply the monotonicity method by upper and lower solutions to deduce some a priori estimates for solutions to the initial-boundary value problems for the semilinear time-fractional diffusion equations. Finally, we consider some initial-boundary value problems for systems of the linear and semilinear time-fractional diffusion equations and prove non-negativity of their solutions under the suitable conditions.

math.AP↗
arXiv2024

Simultaneous uniqueness for a coefficient inverse problem in one-dimensional fractional diffusion equation from an interior point measurement

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order $α\in(0,1)$. We prove the uniqueness for the inverse problem by observation data at one interior point over a finite time interval, provided that a coefficient is known on a subinterval. Our proof is based on the uniqueness in the inverse spectracl problem for a Sturm-Liouville problem by means of the Weyl $m$-function and the spectral representation of the solution to an initial-boundary value problem for the fractional diffusion equation.

math.AP↗
arXiv2024

Inverse coefficient problem for one-dimensional evolution equation vanishing initial condition

We consider an inverse problem of determining a coefficient $p(x)$ of an evolution equation $σ\ppp_tu = a(x)\ppp_x^2u - p(x)u$ for $0 0$ and $T>0$ are arbitrarily given. Our main result is the uniqueness: by assuming that the zeros of initial value $b(x):= u(0,x)$ on $[0, \ell]$ is a finite set and each zero is of order one at most, if two solutions have the same Cauchy data at $x=0$ over $(0,T)$ and the same initial value $b(x)$, then the coefficient $p(x)$ is uniquely determined on $[0,\ell]$.

math.AP↗
arXiv2024

Stable beam operation of approximately 1 mA beam under highly efficient energy recovery conditions at compact energy-recovery linac

A compact energy-recovery linac (cERL) has been un-der construction at KEK since 2009 to develop key technologies for the energy-recovery linac. The cERL began operating in 2013 to create a high-current beam with a low-emittance beam with stable continuous wave (CW) superconducting cavities. Owing to the development of critical components, such as the DC gun, superconducting cavities, and the design of ideal beam transport optics, we have successfully established approximately 1 mA stable CW operation with a small beam emittance and extremely small beam loss. This study presents the details of our key technologies and experimental results for achieving 100% energy recovery operation with extremely small beam loss during a stable, approximately 1 mA CW beam operation.

physics.acc-ph↗
arXiv2024

Determination of the flux terms in a time fractional viscoelastic equation

In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the solution exists, unique and depends continuously on the heat flux. Then the Fréchet differentiability of the cost functional is proved. The Conjugate Gradient Algorithm, based on the gradient formula for the cost functional, is proposed for numerical solution of the inverse flux problem. The numerical examples, both with noise-free and noisy data, provide a clear demonstration of the applicability and accuracy of the proposed method.

math.AP↗
arXiv2024

One-dimensional coefficient inverse problems by transformation operators

We prove the uniqueness for an inverse problem of determining a matrix coefficient $P(x)$ of a system of evolution equations $σ\ppp_t u = \ppp_x^2 u(t,x) - P(x) u(t,x)$ for $0 0$ and $T>0$ are arbitrarily given. The uniqueness results assert that two solutions have the same Cauchy data at $x=0$ over $(0,T)$ and the same initial value or the final value which is positive on $[0,\ell]$, then the zeroth-order coefficient is uniquely determined on $[0,\ell]$. The uniqueness for inverse coefficient problem for a system of evolution equations without boundary conditions over the whole boundary is an open problem even in the one-dimension in the case where only initial value is given as spatial data. Moreover, in the case of the zero initial condition, we prove the uniqueness in the half of the spatial interval.

math.AP↗
arXiv2024

Global and local existence of solutions for nonlinear systems of time-fractional diffusion equations

In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the existence of solutions global in time and the blow-up. Our approach involves the truncation of the nonlinear terms, which enables us to handle all local Lipschitz continuous nonlinear terms, provided their sum is less than or equal to zero. By employing a comparison principle for the corresponding linear system, we establish also the non-negativity of the nonlinear system.

math.AP↗