List of Publications

      ABSTRACT - In this paper, we consider the one-dimensional quasilinear Verigin problem and the relative diffraction problem. The existence, uniqueness and the smoothness of the global solution are discussed. 
 
      ABSTRACT - In this paper, a new transformation is found out to straighten the interface $\Gamma: x=f(y), f\in C^{2+\alpha}([0,a]), f_y|_{y=0,a}=0, \delta0,$ $\delta, l=$constants and a perturbation of the interface is considered for a two dimensional diffraction problem. And the existence, uniqueness and regularity of an approximating Muskat model are proved. 
 
      ABSTRACT - In this paper, the semiconductor system is discussed. The existence and uniqueness of the global solution of the carrier transport problem are obtained. Under the condition that the width in some direction of the domain being sufficiently small, the existence and uniqueness of the solution of the steady states are proved. It is also proved that the solution of the carrier transport problem tends to the solution of the steady problem exponentially when t goes to infinity. 
 
      ABSTRACT - In this paper, we extend the monotone method which is also called upper-lower solution method to the sub-strongly coupled reaction-diffusion system which is without quasimonotone condition required. We construct an iterative monotonous sequence to approach the solution. Some application on this result is involved. 
 
      ABSTRACT - We extend a result of existence of weak solutions to a Dirichlet problem for a class of quasilinear elliptic operators which are weakly coercive with the lower order terms and depend on u and Du nonlinearly. The free term of the equation only belongs to the set of bounded measures. 
 
      ABSTRACT - In this paper, we discuss a class of nonlinear high-order variational inequality systems. We obtain the existence of solution and some regularity results. We introduce a suitable test function, belonging to the closed convex set of the variational inequality, with which we establish the estimate of regularity of the solution by the maximal function technique. We also discuss the behavior of the solution near the free boundary by obtaining some local estimates. 
 
      ABSTRACT - In this paper, we study a non-stationary superconductivity model derived from Ginzburg-Landau macroscopic theory. By using gauge invariance and studying a linear problem with curl boundary conditions, we obtain existence of solutions. The solution is unique in the sense of gauge equivalence. 
 
      ABSTRACT - We consider a drift-diffusion semiconductor system coming from a model of n-GaAs related to Gunn effect, which can be transformed into a nonlinear integrodifferential equation with integral boundary condition. We have obtained the global existence, uniqueness and regularity of the solution. 
 
      ABSTRACT - The paper discusses the asymptotic behaviour of weak solutions $u(t,x)$, as $t \to \infty$, to the boundary value problem for one-dimensional viscoelastic equation with singular memory. The changes of phase are admitted for the problem. One of our results is that $u_t(t,\cdot)\rightharpoonup 0$ weakly in $L^2(0,1)$ as $t\to\infty$. 
 
      ABSTRACT - In this paper, we discuss the regularity of solutions for curl boundary elliptic and parabolic problems and related Ginzburg-Landau superconductivity models. The solutions are smooth up to $C^\infty$ if the boundary and the given data are smooth enough. 
 
      ABSTRACT - The asymptotic behaviour of the solutions of a non-stationary Ginzburg-Landau superconductivity model is discussed. Under suitable choices of gauge, it is proved that, as $t$ tends to infinity, the $\omega-$limit set of the solutions of the evolutionary superconductivity model consists of the solutions of the steady-state problem only. An example of non-convergence is also given for solutions under a particular choice of gauge. 
 
      ABSTRACT - In this note we give an existence result to a class of variational inequalities associated with quasilinear elliptic operators of second order with lower order terms. We prove ``a priori'' estimate by a n extension of the truncation method to the nonlinear case. 
 
      ABSTRACT - In athis paper, we investigate in the existence and uniqueness of a quasilinear elliptic problem with measure data included in the free termd both of equation and boundary. We study first some Sobolev-type imbeddings for T-sets and we use the notion of renormalized solution for having uniqueness. 
 
      ABSTRACT - In this paper, we consider a mixed boundary problem for a class of quasilinear elliptic operators with lower order perturbations and boundary condition which containing nonmonotone discontinuities which correspond to a certain class of multiple valued maps. The free terms of the equation and boundary condition only belong to the set of bounded measures. By using truncation method and others, we obtain existence of the solution of the problem. 
 
      ABSTRACT - A nonlinear spin wave model which is a high order degenerate system with a periodical condition with respect to $t$ has been discussed. By using a parameter $\epsilon$ approximation, the existence of a weak solution is obtained. 
 
      ABSTRACT - We consider the regularity of solutions of a system for  nonlinear arbitrary order variational inequality  with some general concrete closed convex sets. The maximal function method and convergence method are used, and higher integrability of the derivatives is obtained.