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2019 | OriginalPaper | Buchkapitel

2. Dynamic Transition Theory

verfasst von : Tian Ma, Shouhong Wang

Erschienen in: Phase Transition Dynamics

Verlag: Springer International Publishing

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Abstract

This chapter introduces the dynamic transition theory for nonlinear dissipative systems developed recently by the authors. The main focus is to derive a general principle, Principle 1, on dynamic transitions for dissipative systems and to introduce a systematic theory and techniques for studying the types and structure of dynamic transitions.

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Fußnoten
1
We follow here the notation used in Ma and Wang (2005b). In particular, a linear operator L : X 1 → X is called a completely continuous field if L = −A + B : X 1 → X, A : X 1 → X is a linear homeomorphism, and B : X 1 → X is a linear compact operator. Also, we refer the interested readers to classical books, e.g., Kato (1995), for the basic knowledge of linear operators, and to Henry (1981) and Pazy (1983) for semigroups of linear operators and sectorial operators.
 
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Metadaten
Titel
Dynamic Transition Theory
verfasst von
Tian Ma
Shouhong Wang
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-29260-7_2

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