224 Results Found

This paper investigates the existence and location of solutions for a Neumann problem driven by a $(p,q)$ Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic operator, wh...

The Green’s function of the Riquier–Neumann problem for the polyharmonic equation in the unit ball is constructed. Using the obtained Green’s function, an integral representation of the solution to the Riquier–Neumann problem...

In this brief note, we study the problem of asymptotic behavior of the solutions for non-resonant, singularly perturbed linear Neumann boundary value problems $\epsilon y^{″}+ky=f\left(t\right)$, $y^{\prime }\left(a\right)=0$, $y^{\prime }\left(b\right)=0$, $k>0,$ with an indication of poss...

We investigate a generalization of the equation $curl\overrightarrow{w}=\overrightarrow{g}$ to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of...

This paper studies a quasilinear and nonuniformly coercive elliptic Neumann problem with right hand side in $L^1\left(\mathsf{\Omega }\right)$ and boundary data in $L^1(\partial \mathsf{\Omega })$, in the context of Sobolev spaces with variable exponent. We analyze the existence and the...

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral frac...

In this article, we present a nonlocal Neumann boundary value problems for separate sequential fractional symmetric Hahn integrodifference equation. The problem contains five fractional symmetric Hahn difference operators and one fractional symmetric...

This paper is concerned with the stochastic optimal control problem of a 1-dimensional McKean–Vlasov stochastic differential equation (SDE) with reflection, of which the drift coefficient and diffusion coefficient can be both dependent on the s...

This study addresses the theoretical development and computational implementation of probabilistic-statistical methods for solving the stationary problems of two-phase filtration of two immiscible, incompressible fluids in a porous medium. The object...

Green’s functions for linear two-point boundary-value problems subject to non-homogeneous Neumann’s boundary conditions are derived. It is shown that, for the differential operator $L\left(y\right)=y^{″}+ky$ with $k\ne n\pi /L$ where n is a natural n...

We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also pr...

Dunkl operators are a family of commuting differential–difference operators associated with a finite reflection group. These operators play a key role in the area of harmonic analysis and theory of spherical functions. We study the solution of...

In the previous author’s works, a representation of the solution of the Dirichlet boundary value problem for the biharmonic equation in terms of Green’s function is found, and then it is shown that this representation for a ball can be written in the...

In this paper, by using the method of lower and upper solutions and notion of ($I_q$)-stability, we established sufficient conditions for the uniform convergence of the solutions of singularly perturbed Neumann boundary value problems for second-order d...

We propose neural-network-based algorithms for the numerical solution of boundary-value problems for the Laplace equation. Such a numerical solution is inherently mesh-free, and in the approximation process, stochastic algorithms are employed. The ch...

In this paper, we consider the 3D problem of laser-induced semiconductor plasma generation under the action of the optical pulse, which is governed by the set of coupled time-dependent non-linear PDEs involving the Poisson equation with Neumann bound...

Sufficient conditions are obtained for a signed maximum principle for boundary value problems for Riemann–Liouville fractional differential equations with analogues of Neumann or periodic boundary conditions in neighborhoods of simple eigenvalu...

We consider a Neumann problem for the fractional Laplacian involving a nonlocal Choquard-type nonlinearity and Sobolev–Hardy exponent. Under suitable assumptions on the data and using the Nehari manifold method, we discuss the existence problem...

This paper addresses the investigation of an equilibrium problem describing an elastic body with an incorporated thin elastic Timoshenko inclusion, provided that the Neumann boundary condition is imposed on the external boundary of the body. The incl...

We establish the existence of at least three weak solutions for a Neumann $p\left(x\right)$-Laplacian-like problem with two control parameters. Our main result is due to the critical theorem of Bonanno and Marano.

Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann boundary value problems are studied. For the problems under consideration, e...

In this paper, we consider the Neumann elliptic problem $\left({\mathcal{I}}_{\epsilon }\right)$: $-\Delta u+V\left(x\right)u=u^{p-\epsilon }$, $u>0$ in $\mathsf{\Omega }$, $\partial u/\partial \nu =0$ on $\partial \mathsf{\Omega }$, where $\mathsf{\Omega }$ is a bounded smooth domain in ${\mathbb{R}}^n$, $n\ge 3$, $p+1=2n/(n-2)$ is th...

We investigate a Cauchy problem of the modified Helmholtz equation with nonhomogeneous Dirichlet and Neumann datum, this problem is ill-posed and some regularization techniques are required to stabilize numerical computation. We established the resul...

A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provi...

We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinit...

We study an exact controllability problem for a system governed by the heat equation with Neumann boundary control and boundary noise. We reduce the control problem to a moment problem for which we establish sufficient conditions for its resolution.

In this paper, we study the data completion problem for the Cauchy–Stokes equation in a cylindrical domain, $\mathsf{\Omega }$. Neumann and Dirichlet boundary conditions are prescribed on part of the overdetermined boundary, ${\mathsf{\Gamma }}_0$, and the goal is to c...

We consider the Sturm–Liouville equation on a finite interval with a real-valued integrable potential and propose a method for solving the following general inverse problem. We recover the potential from a given set of the output boundary value...

A formulation of an alternating direction implicit (ADI) method is given by extending peaceman and Rachford Scheme to three dimensions. The scheme becomes conditionally stable. The von Neumann stability analysis is performed. Numerical results for so...

Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevanc...

This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant wi...

In this paper, we considered the Neumann elliptic equation $\left({\mathcal{P}}_{\epsilon }\right)$: $-\Delta u+K\left(x\right)u=u^{(n+2)/(n-2)-\epsilon }$, $u>0$ in $\Omega$, $\partial u/\partial \nu =0$ on $\partial \Omega$, where $\Omega$ is a smooth bounded domain in ${\mathbb{R}}^n$, $n\ge 6$, $\mathrm{\&epsi}$...

In this paper, we consider the nonlinear Neumann problem $\left(Q_{\epsilon }\right):-\Delta u+V\left(x\right)u=u^{{\displaystyle \frac{n+2}{n-2}}-\epsilon }$, with $u>0$ in $\Omega$ and $\partial u/\partial \nu =0$ on $\partial \Omega$, where $\Omega$ is a bounded regular domain in ${\mathbb{R}}^n$, with $n\ge 4$,...

In this paper, we consider the nonlinear Neumann problem $\left({\mathcal{P}}_{\epsilon }\right)$: $-\Delta u+V\left(x\right)u=K\left(x\right)u^{(n+2)/(n-2)-\epsilon }$, $u>0$ in $\mathsf{\Omega }$, $\partial u/\partial \nu =0$ on $\partial \mathsf{\Omega }$, where $\mathsf{\Omega }$ is a smooth bounded domain in ${\mathbb{R}}^n$, $n\ge 4$, $\mathrm{\&ep}$...

The inverse problem under consideration concerns a one-dimensional parabolic equation whose thermal diffusivity takes the quadratic-in-space form $a_s\left(\tau \right){\kappa }^2+b_s\left(\tau \right)\kappa +c_s\left(\tau \right)$. The unknowns are three time-dependent coefficients $a_s(\mathrm{\&tau}$...

The work is dedicated to mathematical modelling of random diffusion flows of admixture particles in a two-phase stratified strip with stochastic disposition of phases and random thickness of inclusion-layers. The study of such models are especially i...

This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shan...

This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using surjectivity or variational approaches, one may obtain or characterize we...

This paper deals with Lopatinskii type boundary value problem (bvp) for the (poly) harmonic differential operators. In the case of Robin bvp for the Laplace equation in the ball $B_1$ a Green function is constructed in the cases $c>0$, $c\notin -\mathbf{N}$...

Given a compact Riemannian manifold $(M,g)$ with smooth boundary $\partial M$, we give an explicit expression for the full symbol of the thermoelastic Dirichlet-to-Neumann map ${\mathsf{\Lambda }}_g$ with variable coefficients $\lambda ,\mu ,\alpha ,\beta \in C^{\infty }(\stackrel{}{M}$...

In this paper, in the class of smooth functions, integration and differentiation operators connected with fractional conformable derivatives are introduced. The mutual reversibility of these operators is proved, and the properties of these operators...

This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using the widely debated results of surjectivity or variational approaches, one...

In this paper, we consider the nonlinear elliptic equation $-\Delta u+V\left(x\right)u=g\left(x\right)u^{{\displaystyle \frac{n+2}{n-2}}-\epsilon }$ in a bounded, smooth domain $\Omega$ in ${\mathbb{R}}^n$, under zero Neumann boundary conditions, where $n\ge 4$, $\epsilon$ is a small positive paramete...

We discuss V.P. Belavkin’s approach to the Schrödinger cat problem and show its close relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman. The purpose of the paper is to explain these i...

We consider a dynamic problem with a short laser impact on a semi-opaque insulated layer with free borders, accounting for the selective absorption of the acoustic spectrum regions by the media. The behavior of the material is modeled by the extended...

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the La...

New Monte Carlo algorithms for solving the Cauchy problem for the second order parabolic equation with smooth coefficients are considered. Unbiased estimators for the solutions of this problem are constructed.

In this paper, using the notion of ($I_q$)–stability and the method of a priori estimates, known as the method of lower and upper solutions, the sufficient conditions guaranteeing uniform convergence of solutions to the solution of a reduced probl...

This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to d...

We propose a foundational framework in which internal temporal ordering, the low-entropy boundary of the observable branch, the compatibility of a local thermodynamic arrow with a global partition lifecycle, and a qualitative late-time dark-energy si...