Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions

DOI10.1016/j.jde.2011.09.024zbMath1242.35008OpenAlexW2087880544MaRDI QIDQ649747

Mark Craddock, Kelly A. Lennox

Publication date: 6 December 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.09.024

zbMATH Keywords

Fourier transformsrepresentation theorytransition densities

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Second-order parabolic equations (35K10) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (14)

Fourier type transforms on Lie symmetry groups ⋮ Equivalence and symmetries for variable coefficient linear heat type equations. I ⋮ Equivalence and symmetries for variable coefficient linear heat type equations. II. Fundamental solutions ⋮ New classes of non-convolution integral equations arising from Lie symmetry analysis of hyperbolic pdes ⋮ Lie symmetry methods for local volatility models ⋮ Weak symmetries of stochastic differential equations driven by semimartingales with jumps ⋮ Reduction and reconstruction of stochastic differential equations via symmetries ⋮ Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions ⋮ Symmetry properties and explicit solutions of the nonlinear time fractional KdV equation ⋮ Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations ⋮ Symmetry analysis and exact solutions to the space-dependent coefficient PDEs in finance ⋮ On the equivalence of Lie symmetries and group representations ⋮ Invariant analysis and exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation by Lie group analysis ⋮ Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov–Kuznetsov equation

Uses Software

• DLMF

Cites Work

• Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions
• Sturm and Liouville's work on ordinary linear differential equations. The emergence of Sturm-Liouville theory
• Lie group symmetries as integral transforms of fundamental solutions
• Fundamental solutions to Kolmogorov equations via reduction to canonical form
• On the equivalence of Lie symmetries and group representations
• The calculation of expectations for classes of diffusion processes by Lie symmetry methods
• Fundamental solutions, transition densities and the integration of Lie symmetries
• An introduction to partial differential equations
• Symmetry groups of partial differential equations, separation of variables, and direct integral theory
• The symmetry groups of linear partial differential equations and representation theory. I
• Spectral asymptotics for Sturm-Liouville equations with indefinite weight
• Symmetries of the Fokker-Planck equation with a constant diffusion matrix in 2 + 1 dimensions
• CLOSED FORM SOLUTIONS FOR QUADRATIC AND INVERSE QUADRATIC TERM STRUCTURE MODELS
• Symmetries and differential equations
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