Math

Browse all posts in the Math category.

73 to 78 of 82

22SEP 2020
Math
Nonlocal population balance equations and applications
Nonlocal population balance equations and applications Michele Spinola, FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg Motivational example: look ahead behavior of car drivers When analyzing traffic situations, one possible way to observe the current state is from bird’s eye view. The velocity of a car driver at time at location depends on the traffic density at time : […]
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14SEP 2020
EZuazua
Inverse Design for Hamilton-Jacobi Equations
Inverse Design For Hamilton-Jacobi Equations Carlos Esteve Yagüe, Enrique Zuazua, DeustoCCM, FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg In many evolution models, the reconstruction of the initial state given an observation of the system at time represents a major challenge in mathematical modelling. Especially if it involves irreversible processes, where sometimes, different initial conditions can lead the system […]Inverse Design For Hamilton-Jacobi Equations Carlos Esteve Yagüe, Enrique Zuazua, DeustoCCM, FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg In many evolution models, the reconstruction of the initial state given an observation of the system at time represents a major challenge in mathematical modelling. Especially if it involves irreversible processes, where sometimes, different initial conditions can lead the system […]
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31AUG 2020
Math
Stochastic Neural Dynamics
Stochastic Neural Dynamics Marius Yamakou, FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg Neural activity shows fluctuations and unpredictable transitions in its dynamics. This randomness can be an integral aspect of neuronal function; examples range from discrete fluctuations of ion channels to sudden sleep stage transitions involving the entire brain. To understand brain function as well as dysfunctions (i.e., […]Stochastic Neural Dynamics Marius Yamakou, FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg Neural activity shows fluctuations and unpredictable transitions in its dynamics. This randomness can be an integral aspect of neuronal function; examples range from discrete fluctuations of ion channels to sudden sleep stage transitions involving the entire brain. To understand brain function as well as dysfunctions (i.e., […]
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$Controllability properties of fractional PDE$
23JUL 2020
Math
Controllability properties of fractional PDE
Controllability properties of fractional PDE Umberto Biccari, DeustoCCM Controllability of the fractional heat equation Let be an open and nonempty subset. Consider the following non-local one-dimensional heat equation defined on the domain where is a given initial datum. In (1), for all , denotes the one-dimensional fractional Laplace operator, which is defined as the […]
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09JUL 2020
EZuazua
Flows on Networks
Flows on Networks Enrique Zuazua, Nicola de Nitti, FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg PDE models on Networks In the last few decades, models based on partial differential equations have been very effective in tackling many applied problems dealing with flows on networks. The areas of application include mainly the study of vehicular traffic, supply chains, […]
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24JUN 2020
Math
Stochastic optimization for simultaneous control
Stochastic optimization for simultaneous control Umberto Biccari, DeustoCCM What is a simultaneous control problem? Consider the following parameter-dependent linear control system with The matrix is associated with the Brunovsky canonical form of the linear ODE where denotes the -th derivative of the function . In (1)-(2), , , denotes the state, the matrix […]
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