Article
Mathematics
Evgeny S. Asmolov, Tatiana Nizkaya, Olga Vinogradova
Summary: In this study, we have derived a non-linear outer solution for the electric field and concentrations of catalytic swimmers with any shape, and determined the velocity of particle self-propulsion. Our approach allows us to include the complicated effects of anisotropy and inhomogeneity of surface ion fluxes, leading to more accurate calculations.
Article
Mathematics
Chan Li, Jin Liang, Ti-Jun Xiao
Summary: This research focuses on the asymptotic behaviors of solutions for linear wave equations with frictional damping only on Wentzell boundary, without any interior damping. Through analysis of an associated auxiliary system, an ideal estimate of the resolvent of the system generator along the imaginary axis is obtained, leading to the proof of polynomial decay of system energies. The energy stability result provides a solution in the linear case to a problem proposed by Cavalcanti et al. (2007) due to the lack of interior damping.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Jiayu Li, Fangshu Wan, Yunyan Yang
Summary: In this study, we establish asymptotic expansions of u(x) to arbitrary orders near 0, combining a priori estimate and mathematical induction. Our results complement previous findings on the Yamabe equation, weighted Yamabe equation, and Liouville equation.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2022)
Article
Mathematics, Applied
Kazuhiro Ishige, Tatsuki Kawakami
Summary: In this paper, we improve upon the research conducted by (Ishige et al. in SIAM J Math Anal 49:2167-2190, 2017) by obtaining higher order asymptotic expansions for the large time behavior of solutions to inhomogeneous fractional diffusion equations and nonlinear fractional diffusion equations.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Mifodijus Sapagovas, Jurij Novickij
Summary: This paper considers the stability of the alternating direction method for wave equation with integral boundary conditions in an energy norm. The proof of stability is based on the properties of eigenvalues and eigenvectors of the corresponding difference operators. The main properties of the alternating direction method are theoretically and numerically proven.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Vianey Villamizar, Jacob C. Badger, Sebastian Acosta
Summary: This paper presents derived high order and local absorbing boundary conditions (ABC) for solving multiple acoustic scattering problems in two- and three-dimensional settings. By considering continuities and utilizing the superposition of outgoing waves, a novel ABC is defined at artificial boundaries, exhibiting both accuracy and computational efficiency in dealing with complex-shaped obstacles.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Dimitrios Betsakos, Alexander Solynin
Summary: We investigate the solutions uf to a one-dimensional Robin problem with heat source f and Robin parameter α. The goal is to find the heat sources f0 that maximize the temperature gap max[-π,π]uf - min[-π,π]uf over all heat sources f such that m≤f≤M and ∥f∥L1 = 27rs, where m, M, and s are given with 0≤m<s<M. This result provides an answer to a question raised by J.J. Langford and P. McDonald in [5]. We also analyze the heat sources that maximize/minimize uf at a given point x0∈[-π,π] within the same class of heat sources, and discuss several related questions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Hui Wei, Shuguan Ji
Summary: This study focuses on the periodic solutions of a semilinear variable coefficient wave equation that arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The authors use the invariant subspace method, complete reduction technique, and Leray-Schauder theory to prove the existence of periodic solutions under nonresonance conditions.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Shuaishuai Lu, Xue Yang
Summary: We observe Poisson stable solutions for nonlinear stochastic functional differential equations (SFDEs) with finite delay. Firstly, we prove the existence and uniqueness of bounded (in square-mean sense) solutions and solution maps for SFDEs with finite delay by remote start (or dissipative method) and classical pull-back attraction method. Then, based on the relationship between the solution and coefficients, we obtain such Poisson stable solutions by using Shcherbakov's comparability method in character of recurrence. The solutions of the delay equations are not-Markov, so we employ the solution maps in the appropriate phase space as a viable alternative for studying further asymptotic properties, and we also discuss Poisson stable solution maps and their asymptotic stability. For illustration of our results, we give the application arising from stochastic Lotka-Volterra cooperative systems with distributed delay.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Kazuhiro Takimoto
Summary: This study considers the boundary blowup problem for a k-Hessian equation in a uniformly (k-1)-convex domain, and obtains the asymptotic behavior of a solution near the boundary up to the second order.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Byungjoon Lee, Chohong Min
Summary: MILU preconditioner is considered optimal for solving the Poisson equation with Dirichlet boundary conditions, but the optimal preconditioner for solving with Neumann boundary conditions is less known. The condition number of an unpreconditioned matrix can be significantly reduced by using the optimal preconditioner.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics
Shuaishuai Lu, Xue Yang
Summary: This work investigates Poisson stable solutions for stochastic functional evolution equations (SFEEs) with infinite delay. The existence of bounded mild solutions for SFEEs with infinite delay is proved, and Poisson stable solutions are obtained based on the relationship between the solution and coefficients. As the solutions of the delay equations are not Markov, solution maps are employed to study further asymptotic properties, and the Poisson stable solution maps and their asymptotic stability are discussed.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Chiu-Yen Kao, Seyyed Abbas Mohammadi
Summary: This paper studies both minimization and maximization problems of a Poisson's equation with Robin boundary conditions, analyzing the properties of extremizers and their performance on general domains, as well as investigating the asymptotic behaviors of optimal values. Explicit solutions are rare, but solutions on N-balls are obtained. Numerical efficient algorithms based on finite element methods, rearrangement techniques, and analytical results are proposed to determine extremizers in a few iterations on general domains.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Astronomy & Astrophysics
Gabriel Alvarez, Luis Martinez Alonso, Elena Medina
Summary: In this study, generalized asymptotic solutions for the inflaton field, Hubble parameter, and equation-of-state parameter valid during the oscillatory phase of reheating for potentials behaving as even monomial potentials near their global minima are determined. Specific expressions for the quadratic and quartic potentials are derived, as well as general two-term solutions in the general case, where the leading order term is defined implicitly in terms of the Gauss hypergeometric function. The physical significance of these solutions in the oscillatory regime and their matching to appropriate solutions in the thermalization regime are discussed.
Article
Mathematics, Applied
Yanlin Liu, Li Xu
Summary: In this paper, we study the global existence of a unique strong solution to the 3-D Navier-Stokes equations with almost axisymmetric initial data. We establish refined estimates for the integral average in the θ variable and consider the expansion of the initial data into Fourier series. The asymptotic expansion of the solution is also studied, along with the influence between different profiles.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2023)
