Delay differential equations arise in many applications, and in the case of constant delays solutions give rise to semi-flows on function spaces. A fairly mature theory of such problems as infinite dimensional dynamical systems has now been developed. However, models in physical and biological applications are increasingly encompassing features which do not fit this theory, often having non-constant and state-dependent delays. Mixed type differential equations with both advanced and retarded arguments also arise, for example as the defining equations for travelling waves in nonlinear lattices. Volterra functional (integral and integro-differential) equations with variable and state-dependent delays, including equations of “integral-algebraic” type, are also used with increasing frequency. The theory of such problems is still not complete, though significant progress has been made in recent years. A large gap also exists in the numerical analysis and computational solution of such functional equations.

This workshop will provide a wide perspective on current research and open problems, covering theory, applications and numerical analysis of these equations. Recent advances across the field of DDEs will be covered, with particular concentrations in non-constant delay equations, advance-delay differential equations and Volterra functional equations, including problems with “differential-algebraic” structure. The workshop will bring together specialists in analysis and numerical computations of the functional and delay equations, with particular applications in biological problems and traveling waves in nonlinear lattices.

Concentration Areas

• Dissipative Advanced Retarded Equations
• Hamiltonian Advanced Retarded Equations
• Numerical DDEs (Chinese & Italian schools, numerics also in other concentrations)
• Applications in Mathematical Biology (Mathematical Physiology and Pop Dynamics)
• Volterra and Integral Equations
• State Dependent Delays