About:
Nonlinear Partial Differential Equations are of fundamental importance in mathematics and although major progress in their study has recently been achieved, many profound challenges remain. Developments are motivated not only by advances in pure and applied mathematics but also by new issues in the physical and biological sciences and many other applied disciplines. Themes of the meeting emphasised the importance of partial differential equations in several applied fields including continuum mechanics, microstructure, biology and the dynamics of domain growth.
An important common aspect was the determination of conditions that ensure the equations possess properties that reasonably reflect the expected behaviour of the corresponding physical and other processes. Consequently, investigation of existence, uniqueness and continuous data dependence formed adjunct themes.
During the meeting we celebrated Professor Robin Knops' 80th birthday. Robin was instrumental in establishing the research reputation of the Heriot-Watt Department of Mathematics.
Speakers:
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Jack Carr, Heriot-Watt University - Domain size development in a model of uniform growth in one dimension
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John Ball, University of Oxford - Partial regularity and smooth topology-preserving approximations of rough domains
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Michael Grinfeld, University of Strathclyde - Some aspects of standard and non-standard continuum models of solid-solid phase transitions
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Stephen Watson, University of Glasgow - Emergent Lorenzian-Parabolic coarsening law for driven crystal growth
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Charles Stuart, École Polytechnique Fédérale - Bifurcation of bound states for some elliptic equations on $mathbb{R}^N$
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Alexander Mielke, WIAS - Finite-strain viscoelasticity as a gradient flow
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Oliver Penrose, Heriot-Watt University - How to distinguish the sheep from the goats, or how irreversible PDEs can arise from apparently reversible microscopic dynamics
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Carme Calderer, University of Minnesota - Liquid crystal phase transitions in elastic networks with applications to cytoskeletal modelling
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Brian Straughan, Durham University - Thermal convection in nanofluids