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We construct weak solutions of the anisotropic inverse mean curvature flow (A-IMCF) under very mild assumptions both on the anisotropy (which is simply a norm in $\mathbb R^N$ with no ellip\-ticity nor smoothness requirements, in order to…
This article is devoted to a generalized version of Smoluchowski's coagulation equation. This model describes the time evolution of a system of aggregating particles under the effect of external input and output particles. We show that for…
In this paper we study the following nonlinear Maxwell's equations \\ $\varepsilon \E_{t}+\sigma(x,|\E|)\E= \g \vh +\F,\, \vh_{t}+\g \E=0$, where $\sigma(x,s)$ is a monotone graph of $s$. It is shown that the system has a unique weak…
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…
We prove the existence of global in time, finite energy, weak solutions to a quantum magnetohydrodynamic system (QMHD) with large data, modeling a charged quantum fluid interacting with a self-generated electromagnetic field. The analysis…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
Under the condition of small external forces, we obtain existence of a weak solution of the steady Hall-MHD system with H\"{o}lder continuous magnetic field. We also established regularity of weak solutions provided that magnetic fields are…
This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
We prove the existence, uniqueness, and $W^{1,2}$-regularity for the solution to the Pfaff system with antisymmetric $L^2$-coefficient matrix in arbitrary dimensions. Hence, we establish the equivalence between the existence of…
Considering a two-by-two block operator matrix system of Maxwell type, we present an elementary way of deducing exponential stability under minimal smoothness (and boundedness) requirements of the underlying domains when applications are…
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…
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…
A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the…
This paper revisits the modeling of multicomponent diffusion within the framework of thermodynamics of irreversible processes. We briefly review the two well-known main approaches, leading to the generalized Fick-Onsager multicomponent…
We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a…
We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of…