Amplitude Equations For Stochastic Partial Differential Equations (interdisciplinary Mathematical Sciences)
by Dirk Blomker /
2007 / English / PDF
2.3 MB Download
Rigorous error estimates for amplitude equations are well known for
deterministic PDEs, and there is a large body of literature over
the past two decades. However, there seems to be a lack of
literature for stochastic equations, although the theory is being
successfully used in the applied community, such as for convective
instabilities, without reliable error estimates at hand. This book
is the first step in closing this gap. The author provides details
about the reduction of dynamics to more simpler equations via
amplitude or modulation equations, which relies on the natural
separation of time-scales present near a change of stability. For
students, the book provides a lucid introduction to the subject
highlighting the new tools necessary for stochastic equations,
while serving as an excellent guide to recent research.
Rigorous error estimates for amplitude equations are well known for
deterministic PDEs, and there is a large body of literature over
the past two decades. However, there seems to be a lack of
literature for stochastic equations, although the theory is being
successfully used in the applied community, such as for convective
instabilities, without reliable error estimates at hand. This book
is the first step in closing this gap. The author provides details
about the reduction of dynamics to more simpler equations via
amplitude or modulation equations, which relies on the natural
separation of time-scales present near a change of stability. For
students, the book provides a lucid introduction to the subject
highlighting the new tools necessary for stochastic equations,
while serving as an excellent guide to recent research.