Article
Mathematics
Hongjie Dong, Zongyuan Li
Summary: This study considers the mixed Dirichlet-conormal problem for the heat equation on cylindrical domains with a bounded and Lipschitz base 12 subset of Rd and a time-dependent separation Lambda. Under certain regularity assumptions, it is shown that the mixed problem is solvable in Lq for any q > 1 sufficiently close to 1. Similar results are obtained for q = 1 when the data is in the Hardy space. Under additional conditions, the unique solvability result is proved for any q in the range (1, (m + 2)/(m + 1)), where m = 0, ..., d - 2.
ADVANCES IN MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Oliver Boolakee, Martin Geier, Laura De Lorenzis
Summary: We propose novel, second-order accurate boundary formulations for Dirichlet and Neumann boundary conditions on arbitrary curved boundaries. The proposed methodology is based on the asymptotic expansion technique and is expected to have general applicability beyond the scope of this paper. We develop a modified version of the bounce-back method for Dirichlet boundary conditions, and a novel generalized ansatz for Neumann boundary conditions that requires information from one additional neighbor node.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Physics, Fluids & Plasmas
Katarzyna Bolonek-Lason, Joanna Gonera, Piotr Kosinski
Summary: It is shown that the structure of the symmetry transformations relevant to the superintegrability in Kepler dynamics can be exhibited through an appropriate canonical transformation, which fits nicely into a general scheme of nonlinear realizations. In the new coordinates, the Kepler dynamics can be understood as the dimensional reduction of the description of low-energy mesons with spontaneously broken chiral symmetry.
Article
Mathematics, Applied
Alexander G. Ramm
Summary: This paper proves the existence and uniqueness of the solution to the Dirichlet problem with boundary values in L-1(S). The result is new and the proof method is also new.
Article
Engineering, Mechanical
Jan Plagge, Reinhard Hentschke
Summary: This study reviews theories of rubber friction and proposes a new contact theory. The adhesive contact problem is solved using the boundary element method and friction coefficients are calculated. The results show that adhesion increases friction at low velocities. The influence of filler size is considered and a multi-scale approach is used for modeling.
TRIBOLOGY INTERNATIONAL
(2022)
Article
Mathematics
Ben Goldys, Szymon Peszat
Summary: In this paper, we study inhomogeneous Dirichlet boundary value problems associated with a linear parabolic equation dudt = Au with strongly elliptic operator A, on both bounded and unbounded domains with white noise boundary data. Our main assumption is that the heat kernel of the corresponding homogeneous problem has Gaussian-type estimates based on the distance to the boundary. Under mild assumptions about the domain, we show that A generates a C0-semigroup in weighted Lp-spaces where the weight is a suitable power of the distance to the boundary. We also prove some smoothing properties and exponential stability of the semigroup. Finally, we reformulate the Cauchy-Dirichlet problem with white noise boundary data as an evolution equation in the weighted space and prove the existence of Markovian solutions and invariant measures.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Lauri Oksanen, Tianyu Yang, Yang Yang
Summary: In this paper, a linearized boundary control method is developed for the inverse boundary value problem of the acoustic wave equation. The reconstruction formula and the stability analysis are provided for both zero potential and nonzero potential cases. Numerical experiments are conducted to validate the proposed method.
Article
Mathematics
M. van den Berg, Tom Carroll
Summary: Given an open subset D in R-m with certain properties, the leading asymptotic behavior of the torsion function's L-infinity norm with Neumann and Dirichlet boundary conditions is obtained as ε approaches 0, in terms of the first eigenvalue of the Laplacian. These estimates quantify the non-trap domain result of Burdzy, Chen, and Marshall.
POTENTIAL ANALYSIS
(2021)
Article
Mathematics, Applied
Victor Dods, Corey Shanbrom
Summary: The Kepler-Heisenberg problem discusses the motion of a planet around a sun in the Heisenberg group. The dynamics of the system are at least partially integrable, and zero-energy orbits are found to stratify into three families, with collisions occurring in finite time if at all.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mathematics
Marian Slodicka
Summary: This paper studies a semilinear parabolic equation in 1D with nonlocal boundary conditions, proposing constructive algorithms for solving steady-state and transient problems, demonstrating the well-posedness of the problem using semigroup theory in C-spaces, and validating the theoretical algorithms through numerical experiments.
Article
Mathematics, Applied
H. A. Matevossian
Summary: This study examines the uniqueness of solutions of a biharmonic problem with specific boundary conditions outside a compact set, assuming the general solution has a finite Dirichlet integral. Depending on the parameter a, uniqueness (non-uniqueness) theorems are established and exact formulas for calculating the dimension of the solution space are derived.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Firdous A. Shah, Mohd Irfan, Kottakkaran S. Nisar, R. T. Matoog, Emad E. Mahmoud
Summary: This article proposes a new operational matrix method based on Fibonacci wavelets and block pulse functions for solving time-fractional telegraph equations, yielding precise outcomes and higher computational efficiency compared to current methods.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Mechanical
Nasrya F. Kossoko, Frederic Dubreuil, Benoit Thiebaut, Michel Belin, Clotilde Minfray
Summary: This paper investigates the tribological conditions required to achieve low friction with a diblock PIB-PEG polymer friction modifier in base oil under severe lubrication regimes. The study found a very low friction coefficient at high temperatures, and characterized the formation of a polymer film on rubbing surfaces and its bonding to the steel substrate through polar functions.
TRIBOLOGY INTERNATIONAL
(2021)
Article
Computer Science, Interdisciplinary Applications
A. M. A. Nasar, G. Fourtakas, S. J. Lind, B. D. Rogers, P. K. Stansby, J. R. C. King
Summary: The paper investigates the implementation of high-order velocity and pressure boundary conditions in Eulerian incompressible smoothed particle hydrodynamics, demonstrating high-order accuracy and robustness for Taylor-Couette flow and cellular flow structures. Through analysis, the proposed formulation can achieve higher levels of accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics
Vivina Barutello, Rafael Ortega, Gianmaria Verzini
Summary: The paper aims to study the periodicity and Dirichlet problem of the perturbed Kepler system by combining variational techniques with regularization methods. The existence of critical points in the associated action functional is proven through a non-local change of variables, leading to the demonstration of infinitely many generalized T-periodic solutions for specific cases without symmetry assumptions.
ADVANCES IN MATHEMATICS
(2021)
