Abstract
This chapter introduces the dynamic transition theory for nonlinear dissipative systems developed recently by the authors. The main focus is the derivation of a general principle, Principle 1, on dynamic transitions for dissipative systems and a study of the types and structure of dynamic transitions. Our work is based on Philosophy 2, which states that we should search for a complete set of transition states.
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- 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 reader to classical books such as (Kato 1995) for a basic knowledge of linear operators, and to Henry (1981), Pazy (1983) for semigroups of linear operators and sectorial operators.
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Ma, T., Wang, S. (2014). Dynamic Transition Theory. In: Phase Transition Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8963-4_2
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