Metastable dynamics of interfaces for parabolic-hyperbolic systems
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The phenomenon known as metastability has been widely studied for a large class of evolutive PDEs. From a general point of view, a metastable behavior appears when solutions to a PDE exhibit a first time scale in which they are close to some non-stationary state for an exponentially long time before converging to their asymptotic limit. In particular, through a transient process, a pattern of internal layers is formed from initial data over a short time interval; once this pattern is formed, the subsequent motion of the internal layers towards the steady state is exponentially slow. In this bo...
The phenomenon known as metastability has been widely studied for a large class of evolutive PDEs. From a general point of view, a metastable behavior appears when solutions to a PDE exhibit a first time scale in which they are close to some non-stationary state for an exponentially long time before converging to their asymptotic limit. In particular, through a transient process, a pattern of internal layers is formed from initial data over a short time interval; once this pattern is formed, the subsequent motion of the internal layers towards the steady state is exponentially slow. In this book we describe a general strategy to approach the problem of the slow motion of internal layers for a class of parabolic-hyperbolic systems, including viscous scalar conservation laws and the Jin-Xin system.
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