Motion planning problem for a class of hyperbolic PDEs

Collocated Observer Design Based on Continuum Backstepping for a Class of Hyperbolic PDEs

A collocated observer design approach is addressed, which is based on the continuum backstepping algorithm for partial differential equations (PDEs) with boundary feedback. This observer for a class of hyperbolic PDEs is constructed through an integral form with undetermined kernel functions, combining with the “inverse” Volterra transformation and using the position and velocity of the colloca...

Numerical Analysis of Hyperbolic PDEs

Solving Hyperbolic PDEs in Matlab

and we allow general boundary conditions. Solving PDEs of this generality is not routine and the success of our software is not assured. On the other hand, it is very easy to use and has performed well on a wide variety of problems. Explicit central finite difference methods are quite attractive for hyperbolic PDEs of this generality. We have implemented four: A two-step variant of the Lax-Frie...

Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$

We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions  $ u(x,0) = u_0 (x)$  and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ;  f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...

A Bilateral Obstacle Problem for a Class of Degenerate Parabolic-Hyperbolic Operators

We investigate some inner bilateral obstacle problems for a class of strongly degenerate parabolic-hyperbolic quasilinear operators associated with homogeneous Dirichlet data in a multidimensional bounded domain. We first introduce the concept of an entropy process solution, more convenient and generalizing the notion of an entropy solution. Moreover, the boundary conditions are expressed by us...