BURA SCOPUS

Partial differential Volterra equations

Research outline (useful links)

I am involved in research with Prof. J. R. Whiteman focusing on:

(i) the elliptic Volterra problem, find u such that

(ii) the parabolic Volterra problem, find u such that

and, (iii) the hyperbolic Volterra problem, find u such that

• Space-time problems. In the above A and B(t,s) represent (at most for B) second order partial differential operators, acting in the space variables, with A assumed self-adjoint and properly elliptic. For example, we might have
  
• Pure-time problems. Here A and B(t,s) are simply (possibly matrix valued) funcions of time only. Systems of these types occur after spatial discretization of the space-time problems above.

Such equations arise when modelling physical problems associated with viscoelastic materials such as polymers. For example: (H) arises by combining Newton's second law with a "Hooke's law with memory", and is used to model dynamic response; (V) models the quasistatic response resulting from neglecting inertial effects; and, (P) models the non-Fickian diffusion effect that results from the memory in the constitutive law.

When mathematics is properly supported I hope to make available a detailed synopsis of our research which will include links to relevant reports, publications etc.