Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations

DOI10.1111/sapm.12025zbMath1288.35306OpenAlexW1606185200MaRDI QIDQ5415914

Chang-Zheng Qu, Jing Kang

Publication date: 19 May 2014

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/sapm.12025

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Symmetries, invariants, etc. in context of PDEs (35B06) Quasilinear parabolic equations (35K59)

Related Items (1)

Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions
• Lie group symmetries as integral transforms of fundamental solutions
• Fundamental solutions to Kolmogorov equations via reduction to canonical form
• The calculation of expectations for classes of diffusion processes by Lie symmetry methods
• Fundamental solutions, transition densities and the integration of Lie symmetries
• The integrable nonlinear degenerate diffusion equation \(u_ t=[f(u)u_ x^{-1}_ x\) and its relatives]
• Hodograph-type transformations
• A stability technique for evolution partial differential equations. A dynamical systems approach
• Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source
• Symmetry group methods for fundamental solutions
• Generalized hodograph transformation and its application to free boundary problems.
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• A two-component generalization of the Camassa-Holm equation and its solutions
• Nonlinear partial differential equations in engineering
• Supersonic flow past a symmetrically curved cone
• A Tree of Linearisable Second-Order Evolution Equations by Generalised Hodograph Transformations
• Symmetry groups and fundamental solutions for systems of parabolic equations
• Hodograph Transformations of Linearizable Partial Differential Equations
• Linearizable Hierarchies of Evolution Equations in (1+1) Dimensions
• Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
• Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
• Group Classification and Generalized Conditional Symmetry Reduction of the Nonlinear Diffusion–Convection Equation with a Nonlinear Source
• Vortex Trains in Super-Alfvénic Magnetogasdynamics. Application of Reciprocal-Bäcklund Transformations
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

This page was built for publication: Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations