Studies in Applied Mathematics最新文献

In this paper, we discuss the existence and uniqueness of isolated periodic traveling wave solutions of a family of nonlinear reaction–convection–diffusion equations using the monotonicity of the ratio of Abelian integrals. A numerical study is also presented.

In this work, we present some criteria about the existence and nonexistence of both Puiseux inverse integrating factors $�V$ and Puiseux first integrals $�H$ for planar analytic vector fields having a monodromic singularity. These functions are a wide generalization of their formal $��R�\left[�\right[�x�,�y�\left]�\right]�$ or algebraic counterpart in Cartesian coordinates $��(�x�,�y�)�$. We prove that none of the functions $�H$ and $�V$ can be used to characterize degenerate centers although the existence of $�H$ is a sufficient center condition.

The objective of this work is to derive and analyze a Green–Naghdi model with Coriolis effect and surface tension in nonflat bottom geometry. Gui et al. derive a Green–Naghdi-type model in flat bottom geometry under the gravity and Coriolis effect. Chen et al. proved the existence and uniqueness of solution in Sobolev space under a condition depending on the initial velocity and the Coriolis effect. In this paper, we provide a rigorous derivation of Green–Naghdi model under the influence of the two mentioned effects, with nonflat bottom. After that, the existence and construction of solutions for the derived model will be proved under two alternative conditions: the first one is the same condition as in Chen et al. and Berjawi et al. and the second one concerns only the Coriolis coefficient $�\Omega$ that supposed to be only of order $��O�\left(�\sqrt{�\mu �}�\right)�$. This existence and uniqueness result ameliorate the result of Chen et al. and Berjawi et al. in the sense that no condition on the velocity is needed. We also prove the continuity of the associated flow map.

This paper presents exact, analytical, and numerical solutions to the two-dimensional Casson fluid boundary layer flow over a moving wedge with varying wall temperature. The boundary layer flow of the Casson fluid with varying wall temperature is governed by a system of partial differential equations called Prandtl boundary layer equations modified by Casson fluid. By applying similarity transformations the governing system of partial differential equations is reduced to a system of nonlinear ordinary differential equations called as the Falkner–Skan equation modified by Casson fluid flow with heat transfer (C-FSEHT). In the beginning, an exact solution of the C-FSEHT is obtained for the particular values of physical parameters (i.e., $��\beta �=�-�1�$, $��\text{Pr}�=�\frac{c}{�c�+�1�}�$, $��N�=�0�$, see nomenclature) in terms of two standard functions, namely error function and exponential function. Thus, obtained exact solution is then modified to obtain the analytical solution of C-FSEHT for general values of physical parameters, in terms of power series. The analysis of the asymptotic behavior of the problem, when the wedge velocity is very large ($��\lambda �\to �\infty �$), is performed using the Dirichlet series. A comparative analysis is performed using the Chebyshev collocation technique (CCT) to validate the obtained results in all the scenarios. The effect of governing parameters, which are the Casson parameter $�c$, Hartree pressure gradient parameter $�\beta$

We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite–Padé approximation and interpolation problems. We also study families of multiple orthogonal polynomials obtained by variation of the measures known from the theory of discrete-time Toda lattice equations. We present determinantal proofs of certain fundamental results of the theory, obtained earlier by other authors in a different setting. We also derive quadratic identities satisfied by the polynomials, which are new elements of the theory. Resulting equations allow to present multiple orthogonal polynomials within the theory of integrable systems.

Employing primarily numerical methods, and working in 1D, we seek to determine which of two competing finite-amplitude acoustic models, specifically, those of Blackstock and Diaz et al, best approximates the acoustic special case of the Euler system. Working in the context of the classical signaling problem with sinusoidal input, we perform our assessment using not only velocity profile plots, but also a number of metrics. Our findings show, without equivocation, that the simpler Diaz et al model outperforms Blackstock's vis-à-vis all comparisons performed and metrics considered.

In this paper, we are concerned with ground state solutions to fractional equations with Coulomb potential and critical exponent. The existence of ground state solutions is established under certain conditions by proposing a new analytical method.

This special issue of Studies in Applied Mathematics is dedicated to the 70th birthday of Professor Thanasis Fokas. It contains a selection of papers that all use in some ways the ground-breaking mathematical ideas and techniques introduced by Thanasis over his long and exceptionally prolific career.

More often, in the mathematical literature, the injectivity of the spherical Radon transform (SRT) for compactly supported functions is considered. In this article, an additional condition, for the reconstruction of an unknown function $��f�\in �C�\left(�R^2�\right)�$ (the support can be noncompact) using the circular Radon transform (CRT) over circles centered on a smooth simple curve is found. It is proved that this problem is equivalent to the injectivity of a so-called two-data CRT over circles centered on a smooth curve (can be a segment). Also, we present an inversion formula of the transform that uses the local data of the circular integrals to reconstruct the unknown function. Such inversions are the mathematical base of modern modalities of imaging, such as thermo- and photoacoustic tomography and radar imaging, and have theoretical significance.

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time-Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the application of high-order Finite Element (FE) to certain classes of PDEs, such as diffusion equations and the Navier–Stokes (NS) equations, often leads to numerical instabilities. These instabilities limit the number of valid terms in the series, though the efficiency of time-series integration even when resummation techniques like the Borel–Padé–Laplace (BPL) integrators are employed. In this study, we introduce a novel variational formulation for computing the terms of a TSE associated with a given PDE using higher-order FEs. Our approach involves the incorporation of artificial diffusion terms on the left-hand side of the equations corresponding to each power in the series, serving as a stabilization technique. We demonstrate that this method can be interpreted as a minimization of an energy functional, wherein the total variations of the unknowns are considered. Furthermore, we establish that the coefficients of the artificial diffusion for each term in the series obey a recurrence relation, which can be determined by minimizing the condition number of the associated linear system. We highlight the link between the proposed technique and the Discrete Maximum Principle (DMP) of the heat equation. We show, via numerical experiments, how the proposed technique allows having additional valid terms of the series that will be substantial in enlarging the stability domain of the BPL integrators.