509 research outputs found
Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the (p1,p2,…,pn)-Laplacian
AbstractWe state and prove a generalized Lyapunov-type inequality for one-dimensional Dirichlet quasilinear systems involving the (p1,p2,…,pn)-Laplacian. Our result generalize the Lyapunov-type inequality given in Napoli and Pinasco (2006) [12]
Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback
We use the backstepping method to study the stabilization of a 1-D linear
transport equation on the interval (0, L), by controlling the scalar amplitude
of a piecewise regular function of the space variable in the source term. We
prove that if the system is controllable in a periodic Sobolev space of order
greater than 1, then the system can be stabilized exponentially in that space
and, for any given decay rate, we give an explicit feedback law that achieves
that decay rate
Cross-diffusion systems with entropy structure
Some results on cross-diffusion systems with entropy structure are reviewed.
The focus is on local-in-time existence results for general systems with
normally elliptic diffusion operators, due to Amann, and global-in-time
existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion
systems with an additional Laplace structure. The boundedness-by-entropy method
allows for global bounded weak solutions to certain diffusion systems.
Furthermore, a partial result on the uniqueness of weak solutions is recalled,
and some open problems are presented
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