Some degenerate and quasilinear parabolic systems not in divergence form

This paper deals with positive solutions of degenerate and quasilinear parabolic systems not in divergence form: u_t=u^p(Δu+av), v_t=v^q(Δv+bu), with null Dirichlet boundary conditions and positive initial conditions, where p, q, a and b are all positive constants. The local existence and uniqueness of classical solution are proved. Moreover, it will be proved that all solutions exist globally if and only if ab?λ₁², where λ₁ is the first eigenvalue of −Δ in Ω with homogeneous Dirichlet boundary condition.     

Positive Solutions of a Class of Quasilinear Elliptic Equations in Two-dimensional Exterior Domains

Sufficient conditions for the existence of positive solutions to a class of quasilinear elliptic equations in two-dimensional exterior domains are given.     

Optimal control of the obstacle in a quasilinear elliptic variational inequality

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H² norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established.     

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES＊＊＊

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system.     

COMPLETE REDUCIBILITY FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper we present a necessary and sufficient condition to guarantee the complete reducibility for quasilinear hyperbolic systems and give some examples.     

CONSTRUCTION OF SOLUTIONS TO M-D RIEMANN PROBLEMS FOR A2×2 QUASILINEAR HYPERBOLIC SYSTEM

ＣＯＮＳＴＲＵＣＴＩＯＮＯＦＳＯＬＵＴＩＯＮＳＴＯＭ－ＤＲＩＥＭＡＮＮＰＲＯＢＬＥＭＳＦＯＲＡ２×２ＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＣＨＥＮＳＨＵＸＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＤｅｃｅｍｂｅｒ２６，１９９４．...     

Quasilinear Schrödinger equations with unbounded or decaying potentials

We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations: where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result.     

On the Global Regularity for a Wave-Klein—Gordon Coupled System

In this paper we consider a coupled Wave-Klein—Gordon system in 3D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This...     

Structure of Positive Solutions of Quasilinear Elliptic Equations with Critical and Supercritical Growth

The structure of positive radial solutions to a class of quasilinear elliptic equations with critical and supercritical growth is precisely studied. A large solution and a small solution are obtained for the equations. It is shown that the large solution is unique, its asymptotic behaviour and flat core are also discussed.