Results 51 to 60 of about 676,988 (164)
Well-posedness and ill-posedness of the fifth-order modified KdV equation
Electronic Journal of Differential Equations, 2008 We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. $$displaylines{ partial_t u - partial_x^5u + c_1partial_x^3(u^3) + c_2upartial_x upartial_x^2 u + c_3uupartial_x^3 u =0cr u(x,0)= u_0(x ...
Soonsik Kwon
doaj
Frequency‐dependent contraction rates for the Bayesian method to the inverse source problem
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This paper addresses an inverse source problem for acoustic waves in a range of frequencies. Our study has two main goals. First, although the problem is severely ill‐posed with a logarithmic stability estimate, we demonstrate, through careful analysis of the forward map's singular values, that increasing the frequency range enhances stability,
Pu‐Zhao Kow, Jenn‐Nan Wang
wiley +1 more source
International Journal of Antennas and Propagation, 2013 A microwave imaging method previously developed for tomographic inspection of dielectric targets is extended to three-dimensional objects. The approach is based on the full vector equations of the electromagnetic inverse scattering problem.
Claudio Estatico +2 more
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Geophysical Research Letters, Volume 53, Issue 19, 16 October 2026.Abstract Accurate representation of raindrop size distribution (DSD) is crucial for understanding precipitation microphysics and improving quantitative precipitation forecasting. Conventional methods in numerical models often prescribe the DSD shape parameter as a constant or derive it from empirical relationships based solely on disdrometer ...
Limin Lin +6 more
wiley +1 more source
One-Dimensional Shallow Water Equations Ill-Posedness
MathematicsIn 2071, the Hydraulic community will commemorate the second centenary of the Baré de Saint-Venant equations, also known as the Shallow Water Equations (SWE). These equations are fundamental to the study of open-channel flow.
Tew-Fik Mahdi
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A Unified Block‐Modal Framework for Inverse Source Problems in Heat and Mass Transfer
International Journal for Numerical Methods in Engineering, Volume 127, Issue 19, 15 October 2026.ABSTRACT This work presents a unified block–modal framework for inverse source identification in linear diffusive problems arising in heat and mass transfer. Starting from a general parabolic model with mixed boundary operators, the Classical Integral Transform Technique is employed to project the dynamics onto an orthonormal eigenbasis, yielding a ...
André J. P. de Oliveira +5 more
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Well-posedness and scalarization in vector optimization [PDF]
In this paper we study several existing notions of well-posedness for vector optimization problems. We distinguish them into two classes and we establish the hierarchical structure of their relationships.
Rocca Matteo +2 more
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Instability and Ill-Posedness in Granular Flow
, 1989 Pitman, E. Bruce; Schaeffer, David G.. (1989). Instability and Ill-Posedness in Granular Flow.
Pitman, E. Bruce +3 more
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BioMedical Engineering OnLine, 2010 Background The inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity.
Wang Jiajun, Zou Wei, Feng David
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Applied Research, Volume 5, Issue 5, October 2026.This study introduces a structurally cascaded physics‐informed graph neural network to model tumor microenvironments accurately. By enforcing a directional dependency from mechanical strain to biochemical secretion, the method eliminates unphysical artifacts and significantly improves predictive accuracy for precision healthcare applications.
Xinyuan Chen +2 more
wiley +1 more source