Monodromy and approach to equilibrium for viscoelastic models allowing microstructure
- Prof. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UK
B3 L5 R5220
For certain models of one-dimensional viscoelasticity, there are infinitely many equilibria representing phase mixtures. In order to prove convergence as time tends to infinity of solutions to a single equilibrium, it seems necessary to impose a nondegeneracy condition on the constitutive equation for the stress. The talk will explain this and show how in some cases, the nondegeneracy condition can be proved using the monodromy group of a holomorphic map. This is joint work with Inna Capdeboscq and Yasemin Şengül. John Ball is Professor of Mathematics at Heriot-Watt University, Edinburgh, and formerly Sedleian Professor of Natural Philosophy at Oxford. He is the current President of the Royal Society of Edinburgh, and a former President of the International Mathematical Union. He specializes in the applications of nonlinear analysis to problems of materials science, liquid crystals and computer vision. Among various awards he received the 2018 King Faisal Prize for Science, the 2018 Leonardo da Vinci Award of the European Academy of Sciences and the 2022 De Morgan Medal of the London Mathematical Society.
Overview
Abstract
For certain models of one-dimensional viscoelasticity, there are infinitely many equilibria representing phase mixtures. In order to prove convergence as time tends to infinity of solutions to a single equilibrium, it seems necessary to impose a nondegeneracy condition on the constitutive equation for the stress. The talk will explain this and show how in some cases, the nondegeneracy condition can be proved using the monodromy group of a holomorphic map. This is joint work with Inna Capdeboscq and Yasemin Şengül.
Brief Biography
John Ball is a Professor of Mathematics at Heriot-Watt University, Edinburgh, and formerly a Sedleian Professor of Natural Philosophy at Oxford. He is the current President of the Royal Society of Edinburgh and a former President of the International Mathematical Union. He specializes in the applications of nonlinear analysis to problems of materials science, liquid crystals, and computer vision. Among various awards, he received the 2018 King Faisal Prize for Science, the 2018 Leonardo da Vinci Award from the European Academy of Sciences, and the 2022 De Morgan Medal of the London Mathematical Society.