Our results and approach are related to previous work in the non-obstacle case. In particular, in [2], almost global existence was shown for general, quadratic quasilinear wave equations in Minkowski space, using fully the invariance properties of the wave operator under translations, spatial rotations, scaling, and Lorentz boosts . Subsequently, in [5], the almost global existence of certain d...

In this paper we establish the theory on semiglobal classical solution to first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, and based on this, the corresponding exact boundary controllability and observability are obtained by a constructive method. Moreover, with the linearized Saint-Venant system and the 1D linear wave equation as examples, we show that th...

This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary optimality conditions for the considered problem are established. The computing optimal controls are helped to identify the unknown coefficien...

We consider the problem of boundary stabilization for a quasilinear 2×2 system of first-order hyperbolic PDEs. We design a full-state feedback control law, with actuation on only one end of the domain, and prove local H exponential stability of the closed-loop system. The proof of stability is based on the construction of a strict Lyapunov function. The feedback law is found using the recently ...

in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.

In this paper we obtain the interior C regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local L estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method.