Free Boundary Problems In Pdes And Particle Systems (springerbriefs In Mathematical Physics)
by Errico Presutti /
2016 / English / PDF
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In this volume a theory for models of transport in the presence
of a free boundary is developed.
In this volume a theory for models of transport in the presence
of a free boundary is developed.
Macroscopic laws of transport are described by PDE's.
Macroscopic laws of transport are described by PDE's.
When the system is open, there are several mechanisms to couple
the system with the external forces. Here a class of systems
where the interaction with the exterior takes place in
correspondence of a free boundary is considered. Both continuous
and discrete models sharing the same structure are
analysed.
When the system is open, there are several mechanisms to couple
the system with the external forces. Here a class of systems
where the interaction with the exterior takes place in
correspondence of a free boundary is considered. Both continuous
and discrete models sharing the same structure are
analysed.
In Part I a free boundary problem related to the Stefan Problem
is worked out in all details. For this model a new notion of
relaxed solution is proposed for which global existence and
uniqueness is proven. It is also shown that this is the
hydrodynamic limit of the empirical mass density of the
associated particle system. In Part II several other models are
discussed. The expectation is that the results proved for the
basic model extend to these other cases.
In Part I a free boundary problem related to the Stefan Problem
is worked out in all details. For this model a new notion of
relaxed solution is proposed for which global existence and
uniqueness is proven. It is also shown that this is the
hydrodynamic limit of the empirical mass density of the
associated particle system. In Part II several other models are
discussed. The expectation is that the results proved for the
basic model extend to these other cases.
All the models discussed in this volume have an interest in
problems arising in several research fields such as heat
conduction, queuing theory, propagation of fire, interface
dynamics, population dynamics, evolution of biological systems
with selection mechanisms.
All the models discussed in this volume have an interest in
problems arising in several research fields such as heat
conduction, queuing theory, propagation of fire, interface
dynamics, population dynamics, evolution of biological systems
with selection mechanisms.
In general researchers interested in the relations between PDE’s
and stochastic processes can find in this volume an extension of
this correspondence to modern mathematical physics.
In general researchers interested in the relations between PDE’s
and stochastic processes can find in this volume an extension of
this correspondence to modern mathematical physics.