Article
Mathematics
Giovanni Di Fratta, Alberto Fiorenza
Summary: The paper presents a unified strategy to derive Hardy-Poincare inequalities on bounded and unbounded domains. It extends the approach to variable exponent Sobolev spaces and shows the possibility of a modular form of the Poincare inequality under certain conditions. The concise and constructive argument does not rely on compactness results and retrieves geometric information on the best constants.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Peter I. Kogut, Olga P. Kupenko, Guenter Leugering
Summary: This paper investigates the exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. By studying a relaxed version of the original problem, the existence and uniqueness of solutions are discussed, and conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof are derived using the HUM method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
V. J. Ervin
Summary: This article investigates the regularity of solutions to the fractional diffusion, advection, reaction equation on a bounded domain in R-1. The regularity of the solution is determined by the endpoint behavior of the solution, and it is lower for a sufficiently smooth right hand side function. The regularity of the solution to the fractional diffusion advection reaction equation is two orders lower than that of the fractional diffusion reaction equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
NourElHouda Bourguiba, Ahmed Souabni
Summary: This work provides mathematical preliminaries on the generalized prolate spheroidal wave function (GPSWF), demonstrating the super-exponential decay rate of the singular values of the associated operator and offering local estimates and bounds of the GPSWFs. By applying the spectral properties and associated eigenvalues, the quality of approximation of GPSWFs in a weighted Sobolev space is illustrated. Numerical examples are also presented to showcase the different results of this study.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Julie L. Levandosky
Summary: This paper studies the smoothness properties of solutions to a two-dimensional Kawahara equation and shows that the equation's dispersive nature leads to an increase in regularity for the solution. Specifically, if the initial data possesses certain regularity and sufficient decay, the solution will be smoother than the initial data for a specific time interval.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
A. J. Castro, K. Jabbarkhanov, L. Zhapsarbayeva
Summary: The persistence property of the solution for the nonlinear Schrödinger-Airy equation with initial data in the weighted Sobolev space is studied using the contraction principle.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics
Remy Rodiac, Jean Van Schaftingen
Summary: This study introduces a nonlinear criterion for determining when a function can be expressed as a sum of functions belonging to homogeneous fractional spaces.
STUDIA MATHEMATICA
(2021)
Article
Mathematics, Applied
Feng Liu, Peng Cui
Summary: This paper investigates the boundedness and compactness for variation operators of Calderon-Zygmund singular integrals and their commutators on weighted Morrey spaces and Sobolev spaces, and applies them to Hilbert transform, Hermite Riesz transform, etc.
SCIENCE CHINA-MATHEMATICS
(2022)
Article
Mathematics, Applied
Andrea Zanoni
Summary: This article focuses on the homogenization of the Poisson equation with a reaction term and the eigenvalue problem associated with the generator of multiscale Langevin dynamics. The study extends the theory of two-scale convergence to weighted Sobolev spaces in unbounded domains. Convergence results for the solution of the multiscale problems to their homogenized surrogate are provided. Numerical examples are presented to support the analysis.
IMA JOURNAL OF APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Aigerim Kalybay
Summary: This paper investigates the boundedness of a certain class of Hardy operators with kernels from a second order weighted Sobolev space to a weighted Lebesgue space.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Geochemistry & Geophysics
Hong Li, Haiyang Yu, Nai Cao, Shiqing Cheng, He Tian, Shiying Di
Summary: The study suggests that it is challenging to characterize complex reservoirs using a homogeneous permeability model, and a heterogeneous model that considers permeability differences in tight reservoirs is preferred. Formation fluids coexist in multiple phases, and water saturation has a direct effect on production.
Article
Mathematics, Applied
Roberto de A. Capistrano-Filho, Milena Monique de S. Gomes
Summary: The article investigates the Kawahara equation on a bounded interval, focusing on well-posedness and control problems in weighted Sobolev spaces. Results demonstrate the exact controllability in weighted Sobolev spaces when the control region is a neighborhood of the right endpoint, and the controllability of the Kawahara equation by regions in L-2 Sobolev space.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Bartlomiej Dyda, Michal Kijaczko
Summary: This passage discusses the denseness proof of smooth C-infinity functions in weighted fractional Sobolev spaces and non-weighted spaces on arbitrary open sets under certain conditions on the weight. It also mentions a similar result in non-weighted spaces defined by a kernel similar to x bar right arrow vertical bar x vertical bar(-d-sp), which can be considered as a version of the Meyers-Serrin theorem.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
J. C. de Albuquerque, J. L. Carvalho, A. P. F. Souza Filho
Summary: In this paper, the authors investigate a quasilinear logarithmic N-dimensional equation with radial potentials, which can have singularities, be unbounded or decaying at infinity, and have a nonlinearity that behaves like e(alpha|s|N/(N-1)) at infinity. The key contribution of the paper is a new weighted Trudinger-Moser type inequality.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Engineering, Electrical & Electronic
Lorenzo Miretti, Renato Luis Garrido Cavalcante, Slawomir Stanczak
Summary: This study proposes a modeling framework based on infinite dimensional Hilbert spaces that unifies various covariance models, and solves the channel covariance conversion problem with two simple yet effective set-theoretic algorithms, outperforming existing model-based approaches in terms of accuracy and complexity.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Mathematics, Applied
Paola F. Antonietti, Ilario Mazzieri, Niccolo Dal Santo, Alfio Quarteroni
IMA JOURNAL OF NUMERICAL ANALYSIS
(2018)
Article
Engineering, Multidisciplinary
Paola Gervasio, Alfio Quarteroni
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2018)
Article
Engineering, Multidisciplinary
Stefano Pagani, Andrea Manzoni, Alfio Quarteroni
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2018)
Article
Statistics & Probability
Alfio Quarteroni
STATISTICS & PROBABILITY LETTERS
(2018)
Article
Computer Science, Interdisciplinary Applications
Simone Deparis, Michel O. Deville, Filippo Menghini, Luca Pegolotti, Alfio Quarteroni
COMPUTERS & FLUIDS
(2019)
Article
Mathematics, Applied
N. Dal Santo, S. Deparis, A. Manzoni, A. Quarteroni
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Engineering, Multidisciplinary
N. Dal Santo, S. Deparis, A. Manzoni, A. Quarteroni
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2019)
Article
Biophysics
Stefano Buoso, Andrea Manzoni, Hatem Alkadhi, Andre Plass, Alfio Quarteroni, Vartan Kurtcuoglu
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
(2019)
Article
Engineering, Biomedical
Luca Dede, Filippo Menghini, Alfio Quarteroni
Summary: An idealized computational model of the left human heart was constructed to study blood flow dynamics, aiming to reproduce normal function. The Navier-Stokes equations in the ALE formulation were solved, and the presence of mitral and aortic valves was considered through the resistive method. The study assessed blood flow characteristics through analysis of velocity fields, blood pressure, and other clinically meaningful fluid dynamics indicators.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2021)
Article
Biology
Ivan Fumagalli, Marco Fedele, Christian Vergara, Luca Dede', Sonia Ippolito, Francesca Nicolo, Carlo Antona, Roberto Scrofani, Alfio Quarteroni
COMPUTERS IN BIOLOGY AND MEDICINE
(2020)
Article
Biochemical Research Methods
Francesco Regazzoni, Luca Dede, Alfio Quarteroni
PLOS COMPUTATIONAL BIOLOGY
(2020)
Article
Multidisciplinary Sciences
N. Parolini, L. Dede', P. F. Antonietti, G. Ardenghi, A. Manzoni, E. Miglio, A. Pugliese, M. Verani, A. Quarteroni
Summary: The paper introduces a novel mathematical epidemiological model named SUIHTER, which reproduces the history of the Italian epidemic and validates its predictive capabilities through parameter calibration, demonstrating its suitability for scenario analysis at a national level.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Geochemistry & Geophysics
F. Di Michele, J. May, D. Pera, V Kastelic, M. Carafa, C. Smerzini, I Mazzieri, B. Rubino, P. F. Antonietti, A. Quarteroni, R. Aloisio, P. Marcati
Summary: This paper simulates the earthquake in L'Aquila on April 6, 2009 using an open-source code called SPEED. The results show good agreement with recorded data and demonstrate the potential implications for seismic risk assessment.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Christian Vergara, Simone Stella, Massimiliano Maines, Pasquale Claudio Africa, Domenico Catanzariti, Cristina Dematte, Maurizio Centonze, Fabio Nobile, Alfio Quarteroni, Maurizio Del Greco
Summary: This study assessed a computational tool for estimating electrical activation in the left ventricle of patients with left bundle branch block and possible myocardialfibrosis, with a focus on the latest electrically activated segment (LEAS). The results showed that the tool was able to accurately reproduce electrical activation maps and had excellent agreement in LEAS location.
MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING
(2022)
Article
Engineering, Biomedical
Michele Bucelli, Alberto Zingaro, Pasquale Claudio Africa, Ivan Fumagalli, Luca Dede', Alfio Quarteroni
Summary: We have developed a mathematical and numerical model that simulates the various processes involved in heart function, including electrophysiology, mechanics, and hemodynamics. The model also considers the interactions between the different processes, such as electro-mechanical and mechano-electrical feedback. By using a coupled fluid-structure interaction approach, we are able to represent the three-dimensional nature of the heart muscle and hemodynamics. The model has been validated using a realistic human left heart model and shows qualitative and quantitative agreement with physiological ranges and medical images.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2023)
Article
Mathematics, Applied
Kevin J. Painter, Thomas Hillen, Jonathan R. Potts
Summary: The use of nonlocal PDE models in describing biological aggregation and movement behavior has gained significant attention. These models capture the self-organizing and spatial sorting characteristics of cell populations and provide insights into how animals perceive and respond to their surroundings. By deriving and analyzing these models, we can better understand biological movement behavior and provide a basis for explaining sociological phenomena.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Nicola Bellomo, Massimo Egidi
Summary: This paper focuses on Herbert A. Simon's visionary theory of the Artificial World and proposes a mathematical theory to study the dynamics of organizational learning, highlighting the impact of decomposition and recombination of organizational structures on evolutionary changes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs
Summary: This paper provides an overview of flows with moving boundaries and interfaces (MBI), which include fluid-particle and fluid-structure interactions, multi-fluid flows, and free-surface flows. These problems are frequently encountered in engineering analysis and design, and pose computational challenges that require core computational methods and special methods. The paper focuses on isogeometric analysis, complex geometries, incompressible-flow Space-Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian-Eulerian VMS (ALE-VMS) methods, and special methods developed in connection with these core methods.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)