Applications of Integrable Nonlinear Diffusion Equations in Industrial Modelling

DOI10.1007/978-4-431-54907-9_26zbMath1330.35447OpenAlexW333824112MaRDI QIDQ3455021

Philip Broadbridge

Publication date: 3 December 2015

Published in: The Impact of Applications on Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-4-431-54907-9_26

zbMATH Keywords

grain boundariessurface diffusionintegrable modelsStefan problemsnonlinear diffusioninfiltrationunsaturated flowsteel solidification

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Geometric theory, characteristics, transformations in context of PDEs (35A30) Inverse problems in thermodynamics and heat transfer (80A23) Symmetries, invariants, etc. in context of PDEs (35B06) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (1)

Lie symmetries, reduction and exact solutions of the \((1+2)\)-dimensional nonlinear problem modeling the solid tumour growth

Cites Work

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• The role of symmetry and separation in surface evolution and curve shortening
• Temperature-dependent surface diffusion near a grain boundary
• A similarity solution of a multiphase Stefan problem incorporating general nonlinear heat conduction
• Classical symmetry reductions of nonlinear diffusion-convection equations
• Hodograph Transformations of Linearizable Partial Differential Equations
• New classes of symmetries for partial differential equations
• Non-integrability of non-linear diffusion-convection equations in two-spatial dimensions
• Grain boundary grooving by surface diffusion: an analytic nonlinear model for a symmetric groove
• On a nonlinear reaction-diffusion boundary-value problem: application of a Lie-Bäcklund symmetry
• Heat Conduction in Simple Metals

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