Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions

Abstract

Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional assumption on the state-dependent delay function to guarantee the well posedness. For the constructed dynamical system we study the long-time asymptotic behavior and prove the existence of a compact global attractor.

References in corpus (1)

• Two models of partial differential equations with discrete and distributed state-dependent delays

Cited by in corpus (7)

• Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold
• A condition on delay for differential equations with discrete state-dependent delay
• Dynamics of second order in time evolution equations with state-dependent delay
• Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
• Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses
• Viral infection model with diffusion and state-dependent delay: stability of classical solutions
• Local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays