Equations Of Type Research Articles

Combining Laplace transform and Variational iteration method for solving singular IVPs and BVPs of Lane–Emden type equation

This study uses the combined Laplace transform and variational iteration method to analytically solve initial value problems (IVPs) and boundary value problems (BVPs) of Lane- Emden- equation with singular behaviour at . Initially, this method requires calculating the lagrange multiplayer, and after its value was calculated, it was found to be equal , this method is applying on several problems and the results were improved using Padé approximations, the results were compared with the exact solution by calculating the absolute error value between them.

A conservative Allen–Cahn model for a hydrodynamics coupled phase-field surfactant system

In this study, we develop a model for a binary fluid–surfactant system utilizing a coupling of two kinds conservative Allen–Cahn type equations and the Navier–Stokes equations. To ensure mass conservation, we incorporate hybrid Lagrange multipliers into the two Allen–Cahn type equations. Specifically, for the concentration variable, a global correction using a time-dependent Lagrange multiplier is utilized, while for the binary fluid variable, a space–time dependent Lagrange multiplier is applied to minimize the impact of dynamics of motion by mean curvature. We propose a linear second order scheme for practical solution of the model. Computational tests demonstrate that the proposed model is effective for the binary fluid–surfactant system and is capable of preserving the small features of interfaces.

Qualitative behavior and variant soliton profiles of the generalized [formula omitted]-type equation with its sensitivity visualization

This study delves into the exploration of the dynamics of (3+1)-dimensional Painlevé integrable generalized model from different perspectives, which delineates the evolution of nonlinear phenomena in three spatial dimensions and one temporal dimension, displaying the remarkable Painlevé integrability property. The ϕ6-expansion technique is applied to extract traveling wave solutions in the form of Jacobi elliptic functions. To give physical insights of obtained solutions, we present these solutions through graphs such as 2D, 3D and contour plots. Further, to understand the planar dynamical system, we employ the concepts of bifurcation, chaos theory and sensitivity analysis. Bifurcation analysis reveals the dependence on the solution of a planar dynamical system at critical points. Additionally, the detection of chaotic movements in the perturbed dynamical system is achieved by detecting tools. Also the sensitivity analysis of the model is investigate by three distinct initial conditions. The findings are innovative, valuable and captivating for the readers in exploring this model.

On the formulation and investigation of a boundary value problem for a third-order equation of a parabolic-hyperbolic type

On the formulation and investigation of a boundary value problem for a third-order equation of a parabolic-hyperbolic type

Структура электрического поля в конвективно-турбулентном приземном слое атмосферы

Electrodynamic models of the surface layer of the atmosphere, taking into account turbulent and convective transport, are constructed and studied. The models are based on the so-called total current equation derived from the equations of the theory of the electrode effect in the atmosphere. From the point of view of mathematics, this is a partial differential equation of a parabolic type with variable coefficients. Since in this type of equations the differential operator is not necessarily the Sturm-Liouville operator, in appropriate cases it is necessary to use different approaches to integrating the total current equation. This, in turn, makes it necessary to consider various hypotheses about the ratio of the intensities of local factors that affect the structure of the equation. The paper considers several cases of the model corresponding to the convective turbulent and convective-turbulent electrode layer. Analytical solutions of the stationary equation of the total electric current are obtained. in various approximations. Electric field strength profiles in the surface layer of the atmosphere for various physical conditions are constructed and studied.

Multi-bump solutions to Kirchhoff type equations with exponential critical growth in $$\mathbb {R}^2$$

Multi-bump solutions to Kirchhoff type equations with exponential critical growth in $$\mathbb {R}^2$$

Version [1.1] - [2D-xtDCR-LTBEM: A Fortran code for numerical solutions to the unsteady anisotropic-DCR equation of spatio-temporal coefficients]

Variable coefficient equations are usually used as governing equations for modeling problems which are associated with Functionally Graded Materials (FGM). Version 1.1 - 2D-xtDCR-LTBEM is a Fortran code that can be used to find numerical solutions of two-dimensional (2D) initial–boundary value problems which are governed by the unsteady anisotropic-diffusion convection reaction (DCR)-type and the anisotropic-diffusion reaction (DR)-type equations with a class of space–time dependent coefficients, by utilizing a combined Laplace Transform-Boundary Element Method (LTBEM). This code may provide valuable help for simulation of problems of FGM.

Martingale solutions to stochastic nonlocal Cahn–Hilliard- Navier–Stokes systems with singular potentials driven by multiplicative noise of jump type

Abstract In the diffuse interface theory, the motion of two incompressible viscous fluids and the evolution of their interface are described by the well-known model H. The model consists of the Navier–Stokes equations, nonlinearly coupled with a convective Cahn–Hilliard type equation. Here we consider a stochastic version of the model driven by a noise of Lévy type, and where the standard Cahn–Hilliard equation is replaced by its nonlocal version with a singular (e.g., logarithmic) potential. The case of smooth potentials with arbitrary polynomial growth has been already analyzed in [G. Deugoué, A. Ndongmo Ngana and T. Tachim Medjo, Martingale solutions to stochastic nonlocal Cahn–Hilliard–Navier–Stokes equations with multiplicative noise of jump type, Phys. D 398 2019, 23–68]. Taking advantage of this previous result, we investigate this more challenging and physically relevant case. Global existence of a martingale solution is proved with no-slip and no-flux boundary conditions in both 2D and 3D bounded domains. In the two-dimensional case, we prove the uniqueness of weak solutions when the viscosity is constant.

Port-Hamiltonian descriptor systems are relative generically controllable and stabilizable

AbstractThe present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359–377, 2021) on generic controllability and of Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2022) on relative generic controllability of linear differential-algebraic equations. We extend the result from general, unstructured differential-algebraic equations to differential-algebraic equations of port-Hamiltonian type. We derive results on relative genericity. These findings are the basis for characterizing relative generic controllability of port-Hamiltonian systems in terms of dimensions. A similar result is proved for relative generic stabilizability.

Non-autonomous fractional nonlocal evolution equations with superlinear growth nonlinearities

We carry out an analysis of the existence of solutions for a class of nonlinear fractional partial differential equations of parabolic type with nonlocal initial conditions. Sufficient conditions for the solvability of the desired problem are presented by transforming it into an abstract non-autonomous fractional evolution equation, and constructing two families of solution operators based on the Mittag-Leffler function, the Mainardi Wright-type function and the analytic semigroup generated by the closed densely defined operator −A(⋅). The discussions are based on the fractional power theory as well as the Banach fixed point theorem in the interpolation space Xpυ (0⩽υ<1, 1<p<∞).

Orbital stability of peakons and multi-peakons for a generalized quintic-septic Camassa-Holm type equation

Orbital stability of peakons and multi-peakons for a generalized quintic-septic Camassa-Holm type equation

Існування надзвукових періодичних біжучих хвиль в дискретних рівняннях типу Клейна-Ґордона з нелокальною взаємодією

The article is devoted to discrete Klein-Gordon type equations that describe infinite chains of nonlinear oscillators with nonlocal interactions. This implies that each oscillator interacts with several of its neighbors on both sides. The main result of the article concerns the existence of periodic traveling waves in such equations. Sufficient conditions for the existence of such waves were established using the variational method and the mountain pass theorem.

Degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and applications

In this paper, we show the existence and uniqueness of bounded solutions of the degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and obtain the asymptotics of these solutions. As applications, we give partial answers to the Tosatti-Weinkove conjecture and Demailly-Păun conjecture.

A note on Kazdan–Warner type equations on compact Riemannian manifolds

In this note, we prove an existence result for generalized Kazdan–Warner equations on compact Riemannian manifolds by using the flow approach or the upper and lower solution method. In addition, we give a priori estimates for this type equations.

Approximation for the invariant measure with applications for jump processes (convergence in total variation distance)

In this paper, we establish an abstract framework for the approximation of the invariant probability measure for a Markov semigroup. Following Pagès and Panloup (2022) we use an Euler scheme with decreasing step (unadjusted Langevin algorithm). Under some contraction property with exponential rate and some regularization properties, we give an estimate of the error in total variation distance. This abstract framework covers the main results in Pagès and Panloup (2022) and Chen et al. (2023). As a specific application we study the convergence in total variation distance to the invariant measure for jump type equations. The main technical difficulty consists in proving the regularization properties — this is done under an ellipticity condition, using Malliavin calculus for jump processes.

(N,λ)-periodic solutions to abstract difference equations of convolution type

This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we provide a brief overview of (N,λ)-periodic sequences and introduce several results. Secondly, in terms of applications and main objective, we establish sufficient criteria for both the existence and uniqueness of (N,λ)-periodic mild solutions for abstract difference equations of convolution type. Furthermore, we present illustrative examples to highlight our key findings.

A mean field type equation on vector bundles

A mean field type equation on vector bundles

Bubble Point Measurements of cis-1,1,1,4,4,4-Hexafluorobutene [R-1336mzz(Z)] + trans-1,2-Dichloroethene [R-1130(E)] mixtures

Saturation pressures of pure R-1336mzz(Z) and R-1130(E) and bubble point pressures of three R-1336mzz(Z)/1130(E) blends were measured from 265 K to 360 K. For each pure refrigerant or refrigerant blend, a total of twenty unique saturation pressures or bubble points were measured. In total 100 unique state points were obtained. Presently, no Helmholtz-energy-explicit type equation of state (EoS) is available for R-1130(E). While an extended corresponding states EoS for R-1130(E) is available to estimate the properties of the R-1336mzz(Z)/1130(E) blend, this model does not resolve the azeotropic behavior of the mixture. Therefore, the perturbed-chain statistical-associating fluid theory (PC-SAFT) EoS is used to model the vapor–liquid equilibria of the R-1336mzz(Z)/1130(E) blend. PC-SAFT model parameters are reported, and the overall performance of the model is characterized by deviations from the experimental data.

On stability in probability for a cooperative system of two equations with Nicholson’s growth and distributed delay under stochastic perturbations

A method of stability investigation for stochastic nonlinear dynamical systems is demonstrated on a system of two connected Nicholson’s blowflies type equations with distributed delay and exponential nonlinearity. It is supposed that this system is affected by stochastic perturbations of the white noise type that are directly proportional to the deviation of the system state from its equilibrium. Stability conditions for the zero and positive equilibria of the system under consideration are obtained by virtue of the general method of Lyapunov functionals construction and are formulated in terms of Linear Matrix Inequalities (LMIs), that can be checked by MATLAB. Numerical examples and figures illustrate the obtained theoretical results. The described method can be applied in various applications to many stochastic systems of higher dimensions with different types of high-order nonlinearities and different forms of delays.

Exact analytical soliton solutions of the M-fractional Akbota equation

In this paper we explore the new analytical soliton solutions of the truncated M-fractional nonlinear (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional Akbota equation by applying the expa\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp _a$$\\end{document} function technique, Sardar sub-equation and generalized kudryashov techniques. Akbota is an integrable equation which is Heisenberg ferromagnetic type equation and have much importance for the analysis of curve as well as surface geometry, in optics and in magnets. The obtained results are in the form of dark, bright, periodic and other soliton solutions. The gained results are verified as well as represented by two-dimensional, three-dimensional and contour graphs. The gained results are newer than the existing results in the literature due to the use of fractional derivative. The obtained results are very helpful in optical fibers, optics, telecommunications and other fields. Hence, the gained solutions are fruitful in the future study for these models. The used techniques provide the different variety of solutions. At the end, the applied techniques are simple, fruitful and reliable to solve the other models in mathematical physics.