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Personal profile

Research interests

Qualitative behaviour of solutions to initial boundary value problems for various linear and nonlinear theories in continuum mechanics,including elasticity and Navier-Stokes. There is especial current interest in uniqueness, dynamic and spatial stability, continuous data dependence (Saint-Venant's principle), and singularities (dislocations).

Biography

Former Head of Mathematics Department and Vice-Principle , Heriot-Watt University. Former Leverhulme Emeritus Research Fellow Visiting Professorships at Cornell University, University of California at Berkeley. Univeristies of Pisa, Rome III, and EPFL, Lausanne. Past President of Edinburgh Mathematical Society; International Society for the Interaction of Mathematics and Mechanics. Past Series Editor for C&H/CRC Press.

Fingerprint Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

Saint-Venant's Principle Mathematics
Continuous Dependence Mathematics
Differential Inequalities Mathematics
Elastic Material Mathematics
Decay Mathematics
Uniqueness Mathematics
Zero Mathematics
Elastostatics Mathematics

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Research Output 1973 2019

On the Structure of Linear Dislocation Field Theory

Acharya, A., Knops, R. J. & Sivaloganathan, J., 8 Jun 2019, In : Journal of the Mechanics and Physics of Solids.

Research output: Contribution to journalArticle

plastic properties
boundary value problems
traction
screw dislocations
uniqueness

The Filon construct for moving dislocations

Acharya, A. & Knops, R. J., Apr 2018, In : Journal of Engineering Mathematics. 109, 1, p. 239-257 19 p.

Research output: Contribution to journalArticle

Open Access
File
Dislocation
Edge dislocations
Screw dislocations
Boundary value problems
Tensors

New frontiers in Zanaboni's formulation of Saint-Venant's principle

Knops, R. J., 2017, In : Rendiconti Lincei - Matematica e Applicazioni . 28, 2, p. 255-275 21 p.

Research output: Contribution to journalArticle

Saint-Venant's Principle
Piezoelectricity
Thermoelasticity
Dissipative Systems
Coupled System

Spatial decay in transient heat conduction for general elongated regions

Knops, R. J. & Quintanilla, R., 5 Dec 2017, In : Quarterly of Applied Mathematics. 76, 4, p. 611-625 15 p.

Research output: Contribution to journalArticle

Open Access
File
Transient Heat Conduction
Heat conduction
Decay
Maximum principle
Thermal energy

Manifolds in a theory of microstructures

Capriz, G. & Knops, R. J., 2015, Differential Geometry and Continuum Mechanics. Chen, G-Q. G., Grinfeld, M. & Knops, R. J. (eds.). Springer International Publishing, Vol. 3. p. 167-201 35 p. (Springer Proceedings in Mathematics & Statistics; vol. 137).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Microstructure
Hamiltonian Formulation
Noether
Cartesian product
Kinetic energy