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A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals
By means of Muskhelishvili’s method and the technique of generalized conformal map**, the physical plane problems are transformed into regular...
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One-Dimensional Variational Problems
This chapter is devoted to one of the most classical classes of variational problems, the one-dimensional case.
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General one-dimensional model of the time-fractional diffusion-wave equation in various geometries
This paper deals with the analysis of the time-fractional diffusion-wave equation as one-dimensional problem in a large plane wall, long cylinder,...
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The Impact of Frequency Bandwidth on a One-Dimensional Model for Dispersive Wave Turbulence
We combine theory and high-resolution direct numerical simulation to resolve a long-standing puzzle concerning the forced–dissipative statistics of a...
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On Solutions of the One-Dimensional Goldshtik Problem
AbstractA one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a...
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Lattice Boltzmann Model for One-Dimensional Hemodynamic Equations with Friction Force
AbstractIn this paper a lattice Boltzmann model for the one-dimensional blood flow equations in elastic vessels is considered. The method for the...
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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
AbstractIn this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential...
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Dynamics of One-Dimensional Maps and Gurtin–Maccamy’s Population Model. Part I. Asymptotically Constant Solutions
Motivated by the recent work by Ma and Magal [Proc. Amer. Math. Soc. (2021); https://doi.org/10.1090/proc/15629 ] on the global stability property of...
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One-dimensional Barenblatt-type solutions and related inequalities
We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations, and one-dimensional...
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One-Dimensional Branching Processes
A one-dimensional CB-process is a Markov process with branching property taking values in the positive half line. A more general model is the...
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Approximation of One-Dimensional Darcy–Brinkman–Forchheimer Model by Physics Informed Deep Learning Feedforward Artificial Neural Network and Finite Element Methods: A Comparative Study
In the last few years, a new research program such as deep learning neural networks (or simulated neural networks )—a class of machine learning...
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Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects
The exact solutions for the propagation of Love waves in one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) nanoplates with surface...
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How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space
We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired...
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Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating
In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure...
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The Calculus of Variations for One-dimensional Problems
The goal of this chapter is to study one-dimensional variational problems where one tries to minimize an integral functionalIntegral functional of...
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Global Stability to Steady Supersonic Rayleigh Flows in One-Dimensional Duct
Heat exchange plays an important role in hydrodynamical systems, which is an interesting topic in theory and application. In this paper, the authors...
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On the One-Dimensional Asymptotic Models of Thin Neumann Lattices
We consider the spectral Neumann problem for the Laplace operator on a thin lattice comprised of nodes and ligaments. We pose the classical Pauling...
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The existence and stability of spikes in the one-dimensional Keller–Segel model with logistic growth
It is well known that Keller–Segel models serve as a paradigm to describe the self aggregation phenomenon, which exists in a variety of biological...
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Construction of One-Dimensional Diffusions by Semigroups
This chapter contains a treatment of Feller’s seminal contribution to a comprehensive theory of one-dimensional diffusions.
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Complex WKB Method (One-Dimensional Linear Problems on the Complex Plane)
AbstractThe survey is devoted to the complex WKB method which arose as an approach to describing the asymptotic behavior of solutions to...
