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Dynamic Transition Theory

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Phase Transition Dynamics

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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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Notes

  1. 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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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Sichuan, China

    Tian Ma

  2. Department of Mathematics, Indiana University, Bloomington, IN, USA

    Shouhong Wang

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  1. Tian Ma
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  2. Shouhong Wang
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Ma, T., Wang, S. (2019). Dynamic Transition Theory. In: Phase Transition Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-29260-7_2

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