相关论文: Stationary solutions to the two-dimensional Broadw…
In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…
It is shown that bound state solutions of the one dimensional Bogoliubov-de Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on the space coordinate. The existence of bound states in continuum (BIC) like solutions…
Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and…
We consider a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. We study solutions in the space $L^{1}(\mathbb{R}^{3}\times \mathbb{T}^3).$ Special…
Consider the Landau equation with Coulomb potential in a periodic box. We develop a new $L^{2}\rightarrow L^{\infty }$ framework to construct global unique solutions near Maxwellian with small $L^{\infty }\ $norm. The first step is to…
We study a one-dimensional model for granular gases, the so-called Inelastic Maxwell Model. We show theoretically the existence of stationary solutions of the unforced case, that are characterized by an infinite average energy per particle.…
A new volumetric-type boundary treatment is introduced for the lattice Boltzmann method. Populations are projected onto a discontinuous piecewise linear basis and streamed using an exact geometrical mapping. The method is implemented in 2D…
This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of a novel Lyapunov function along with the…
We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces…
The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space of functions bounded by Maxwellians. The…
In this paper we study existence and asymptotic behavior of solitary-wave solutions for the generalized Shrira equation, a two-dimensional model appearing in shear flows. The method used to show the existence of such special solutions is…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
We obtain new $L^1$ contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or non-local diffusion terms. As opposed to…
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a…
The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…
We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for…
For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients $\mathbf A, \mathbf b,\gamma$ in $L^\infty$ and symmetric and uniformly positive definite coefficient matrix $\mathbf A$, this paper…
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous…