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Evolutionary Games in Space

N. Kronik, Y. Cohen (2009)

Mathematical Modelling of Natural Phenomena

The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop...

Evolutionary problems in non-reflexive spaces

Martin Kružík, Johannes Zimmer (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.

Exact boundary controllability of 3-D Euler equation

Olivier Glass (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.

Exact boundary controllability of a nonlinear KdV equation with critical lengths

Jean-Michel Coron, Emmanuelle Crépeau (2004)

Journal of the European Mathematical Society

We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.

Exact boundary controllability of coupled hyperbolic equations

Sergei Avdonin, Abdon Choque Rivero, Luz de Teresa (2013)

International Journal of Applied Mathematics and Computer Science

We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.

Exact boundary observability for quasilinear hyperbolic systems

Tatsien Li (2008)

ESAIM: Control, Optimisation and Calculus of Variations

By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.

Exact boundary synchronization for a coupled system of 1-D wave equations

Tatsien Li, Bopeng Rao, Long Hu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Several kinds of exact synchronizations and the generalized exact synchronization are introduced for a coupled system of 1-D wave equations with various boundary conditions and we show that these synchronizations can be realized by means of some boundary controls.

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