相关论文: On a singular limit problem for nonlinear Maxwell'…

In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type $(P)$ (see below) involving singular nonlinearity and singular weights in smooth…

We give conditions that guarantee uniqueness of renormalized solutions for the Maxwell-Stefan system. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we…

Using the simple case of Blasius similarity solution, we illustrate a recently developed general method that reduces a strongly nonlinear problem into a weakly nonlinear analysis. The basic idea is to find a quasi-solution $F_0$ that…

We study the quasineutral limit for the relativistic Vlasov-Maxwell system in the framework of analytic regularity. Following the high regularity approach introduced by Grenier [44] for the Vlasov-Poisson system, we construct local-in-time…

In mimetic gravity, we derive $D$-dimension charged black hole solutions having flat or cylindrical horizons with zero curvature boundary. The asymptotic behaviours of these black holes behave as (A)dS. We study both linear and nonlinear…

It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…

In this note we explore monodromy defects for non-invertible symmetries in Maxwell theory, exploiting the conformal mapping to $AdS_{3} \times S^{1}$. With this approach we recover the spectrum of the defect conformal primaries. We also…

We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…

New exact solution of the cylindrically symmetric Einstein-Maxwell equations is presented. The solution is singular on the axis of symmetry and at the radial infinity, where sources should be placed. The accepted source at the origin can be…

Given a symmetric Riemannian manifold (M, g), we show some results of genericity for non degenerate sign changing solutions of singularly perturbed nonlinear elliptic problems with respect to the parameters: the positive number {\epsilon}…

We consider the perturbed sine-Gordon equation $\theta_{tt}-\theta_{xx}+\sin \theta= \varepsilon^2 f(\varepsilon x)$, where the external perturbation $\varepsilon^2 f(\varepsilon x)$ corresponds to a small, slowly varying electric field. We…

We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is…

We consider the mixed local-nonlocal semi-linear elliptic equations driven by the superposition of Brownian and L\'evy processes \begin{equation*} \left\{ \begin{array}{ll} - \Delta u + (-\Delta)^s u = g(x,u) & \hbox{in $\Omega$,} u=0 &…

Suppose that $G=(V, E)$ is a connected locally finite graph with the vertex set $V$ and the edge set $E$. Let $\Omega\subset V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph $G$ $$ \left \{…

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…

We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…

We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \epsilon^2 \Delta \psi + V(x) \psi = |\psi|^{p-1} \psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an…

We study a class of nonautonomous, linear, parabolic equations with unbounded coefficients on $\mathbb R^{d}$ which admit an evolution system of measures. It is shown that the solutions of these equations converge to constant functions as…

In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an…

Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance…