Stability of well-posed stochastic evolution equation

On Well-Posed Stochastic Formulations of Optical Flow

Regularization and frequency-domain stability of well-posed systems

We study linear control systems with unbounded control and observation operators using certain regularization techniques. This allows us to introduce a modification of the transfer function for the system also if the input and output operators are not admissible in the usual sense. The modified transfer function is utilized to show exponential stability of sufficiently smooth solutions for the ...

Polynomial Internal and External Stability of Well-posed Linear Systems

We introduce polynomial stabilizability and detectability of well-posed systems in the sense that a feedback produces a polynomial stable C0–semigroup. Using these concepts, the polynomial stability of the given C0–semigroup governing the state equation can be characterized via polynomial bounds on the transfer function. We further give sufficient conditions for polynomial stabilizability and d...

A new well-posed nonlocal Perona-Malik type equation

A modification of the Perona-Malik equation is proposed for which the local nonlinear diffusion term is replaced by a nonlocal term of slightly reduced “strength”. The new equation is globally well-posed (in spaces of classical regularity) and possesses desirable properties from the perspective of image processing. It admits characteristic functions as (formally linearly “stable”) stationary so...

Well-Posed Initial-Boundary Evolution in General Relativity

The waveform emitted in the inspiral and merger of a relativistic binary is theoretical input crucial to the success of the fledgling gravitational wave observatories. A computational approach is necessary to treat the highly nonlinear regime of a black hole or neutron star collision. Developing this computational ability has been the objective of the Binary Black Hole (BBH) Grand Challenge [1]...