相关论文: On a Quasilinear Parabolic-Hyperbolic System Arisi…

We discuss an evolution free boundary problem of mixed type with two free boundaries modeling an idealized electrostatically actuated MEMS device. While the electric potential is the solution of an elliptic equation, the dynamics of the…

We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition…

Regimes with a singular peaking for a wide class of quasilinear second order parabolic equations are studied. On the basis of energy methods, precise estimates of a final profile of a weak solution in a neighborhood of the peaking time are…

In this paper we study quasilinear elliptic systems driven by variable exponent double phase operators involving fully coupled right-hand sides and nonlinear boundary conditions. The aim of our work is to establish an enclosure and…

We prove global existence for quasilinear wave equations outside of a wide class of obstacles. The obstacles may contain trapped hyperbolic rays as long as there is local exponential energy decay for the associated linear wave equation.…

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

A threshold result was proved in this paper for semilinear parabolic system with pure power type nonlinearities

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…

In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment…

Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…

In this paper we investigate the zero-relaxation limit of the following multi-D semilinear hyperbolic system in pseudodifferential form: W_{t}(x,t) + (1/epsilon) A(x,D) W(x,t) = (1/epsilon^2) B(x,W(x,t)) + (1/epsilon) D(W(x,t)) + E(W(x,t)).…

The paper studies the long time behavior of a system that describes the motion of a piece of elastic membrane driven by surface tension and inner air pressure. The system is a degenerate quasilinear hyperbolic one that involves the mean…

This paper is devoted to studying a multi-objective control problem for a class of multi-dimensional quasi-linear parabolic equations. The considered system is driven by a leader control and two follower controls. For each leader control, a…

The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…

We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We…

Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…

We consider backward problems for semilinear coupled parabolic systems in bounded domains. We prove conditional stability estimates for linear and semilinear systems of strongly coupled parabolic equations involving general semilinearities.…

This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on size of the object and the wave length. To this end, two…

A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at different electrostatic potentials. It couples a second order…