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In this paper, we establish the global existence of strong solutions for the 3D viscous, compressible, and heat conducting magnetohydrodynamic (MHD) flows with density-temperature-dependent viscosities in a bo...
As early as 1910, Weyl gave a classification of the singular Sturm–Liouville equation, and divided it into the Limit Point Case and the Limit Circle Case at infinity. This led to the study of singular Sturm–Li...
In this paper, we consider the small-convection limit of chemotaxis-Navier–Stokes system with logarithmic sensitivity and logistic-type source
In this paper, we discuss the oscillatory behavior of solutions of a class of Super-linear fourth-order differential equations with several sub-linear neutral terms using the Riccati and generalized Riccati tr...
Recently, Hattori–Lagha established the global existence and asymptotic behavior of the solutions for a three-dimensional compressible chemotaxis system with chemoattractant and repellent (Hattori and Lagha in...
In this paper, we establish a delayed semilinear plankton system with habitat complexity effect and Neumann boundary condition. Firstly, by using the eigenvalue method and geometric criterion, the stability of...
In this note we consider boundary point principles for partial differential inequalities of elliptic type. First, we highlight the difference between the conditions required to establish classical strong maxim...
In this paper, the Dirichlet problem of Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entire r...
A viscous fourth-order parabolic equation with boundary degeneracy is studied. By using the variational method, the existence of a time-discrete fourth-order elliptic equation with homogeneous boundary conditi...
In our paper, we consider the mixed problem in the context of the Green-Naghdi theory of thermoelastic Cosserat media. Using very accessible mathematical calculations, we prove two qualitative results on the s...
This paper deals with a class of nonlinear scalar field equations with an inhomogeneous perturbation. Two positive solutions were obtained using the variational methods.
In this paper, we prove the existence and uniqueness of solutions for the nonlocal boundary value problem (BVP) using Caputo fractional derivative (CFD). We derive Green’s function and give some estimation for...
In this paper, the existence of a solution for an anisotropic variable exponent system is obtained and proved under general hypotheses. By considering additional conditions, it is proved a multiplicity result....
In this paper, we consider a viscoelastic von Karman equation with damping, delay, and source effects of variable exponent type. Firstly, we show the global existence of solution applying the potential well me...
The paper aims to consider a class of p-Laplacian elliptic systems with a double Sobolev critical exponent. We obtain the existence result of the above problem under the Neumann boundary for some suitable range o...
We study the optimal feedback control for fractional evolution equations with a nonlinear perturbation of the time-fractional derivative term involving Caputo fractional derivatives with arbitrary kernels. Fir...
In this paper, a modified cross-diffusion Leslie–Gower predator–prey model with the Beddington–DeAngelis functional response is studied. We use the linear stability analysis on constant steady states to obtain...
We are concerned with the existence and nonexistence of global weak solutions for a certain class of time-fractional inhomogeneous pseudo-parabolic-type equations involving a nonlinearity of the form
In this paper, we investigate the three-dimensional Cauchy problem of the compressible quantum magnetohydrodynamic model. It is proved that the system admits a unique global solution, provided that the initial...
The object of this paper is to develop an accurate combined spectral collocation approach to numerically solve the generalized nonlinear Benjamin–Bona–Mahony–Burgers equation. The first stage is devoted to dis...
In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution o...
We present a new procedure for the numerical study of the wave equation. We use the spectral discretization method associated with the Euler scheme for spatial and temporal discretization. A detailed numerical...
A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stabi...
The numerical analysis of the temporal distributed and spatial Riesz fractional problem (TDSRFP) is presented in this work. To address the two independent variables, the suggested technique employs a completel...
We study the problem of plasma geometry control problem in a tokamak. The domain location and shape are determined using an approach based on the Kohn–Vogelius formulation and topological asymptotic method. We...
In this manuscript an existence result for an anisotropic variable problem which is related to several applications is proved. By considering suitable hypotheses, the multiplicity of solutions is obtained. Exa...
In this paper, we consider two internal stabilization problems for the multi-dimensional wave equation with a boundary time-delay. We prove that the first problem is well-posed in an appropriate functional spa...
We present the theory of a new fractional Sobolev space in complete manifolds with variable exponent. As a result, we investigate some of our new space’s qualitative properties, such as completeness, reflexivi...
In this paper, we address the Hall-MHD equations with partial dissipation. Applying some important inequalities (such as the logarithmic Sobolev inequality using BMO space, bilinear estimates in BMO space, You...
In this paper, we propose an optimal control problem for an HIV infection model with cellular and humoral immune responses, logistic growth of uninfected cells, cell-to-cell spread, saturated infection, and cu...
We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at ...
We investigate the free-boundary problem of a steadily advancing meniscus in a circular capillary tube. The problem is described using the “interface formation model,” which was originally introduced with the ...
In this paper, we study a class of initial value problems for a nonlinear implicit fractional differential equation with nonlocal conditions involving the Atangana–Baleanu–Caputo fractional derivative. The app...
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