NON-LOCAL PDES WITH DISCRETE STATE-DEPENDENT DELAYS: WELL-POSEDNESS IN A METRIC SPACE

作者：Rezounenko Alexander V^*; Zagalak Petr

来源：Discrete and Continuous Dynamical Systems, 2013, 33(2): 819-835.

DOI：10.3934/dcds.2013.33.819

• PDEs
• state-dependent delay
• solution manifold
• global attractor

Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of continuously differentiable (with respect to an appropriate norm) functions is used to construct a dynamical system. This subset is an analogue of the solution manifold proposed for ordinary equations in [H.-O. Walther, The solution manifold and C-1-smoothness for differential equations with state-dependent delay, J. Differential Equations, 195(1), (2003) 46-65]. The existence of a compact global attractor is proven. As far as applications are concerned, we consider the well known Mackey-Glass-type equations with diffusion, the Lasota-Wazewska-Czyzewska model, and the delayed diffusive Nicholson's blowflies equation, all with state-dependent delays.

• 出版日期2013-2