Generalized Separation of Variables in Nonlinear Heat and Mass Transfer Equations
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Andrei D. Polyanin
Abstract
We outline generalized separation of variables as applied to nonlinear second-order partial differential equations (PDEs). In this context, we suggest a method for constructing exact solutions of nonlinear PDEs. The method involves searching for transformations that “reduce the dimensionality” of the equation. New families of exact solutions of 3D nonlinear elliptic and parabolic equations that govern processes of heat and mass transfer in inhomogeneous anisotropic media are described. Moreover, the method makes it possible to construct exact solutions of nonlinear wave equations. We also present solutions for three families of equations with logarithmic heat sources; the solutions are obtained by nonlinear separation of variables.
Copyright (c)2000 by Walter de Gruyter GmbH & Co. KG
Articles in the same Issue
- Guest Editorial
- On the Role of Porosity in the Stokes Flow Around a Solid Particle
- Permanent Excitation of Standing Gravity Surface Waves by the Resonant Coalescence of Non-Coalescent Cold and Hot Pure Liquid
- Molecular Description of the Surface Tension of Curved Interfaces
- The Effect of Surfactants on Marangoni Convection in the Isobutanol/Water System
- Generalized Separation of Variables in Nonlinear Heat and Mass Transfer Equations
- Chaos and Hyperchaos in a Model of the Belousov-Zhabotinsky Reaction in a Batch Reactor
- Anomalous Damping of Capillary Waves With Surfactant Solutions
- A New Discrete Model for the Non-Isothermic Dynamics of the Exothermic CO-Oxidation on Palladium Supported Catalyst
- Foam Microgeometry
- Instabilities By Local Heating Below an Interface
- Oscillatory Instability and High-Frequency Wave Modes in a Marangoni-Bénard Layer with Deformable Free Surface
Articles in the same Issue
- Guest Editorial
- On the Role of Porosity in the Stokes Flow Around a Solid Particle
- Permanent Excitation of Standing Gravity Surface Waves by the Resonant Coalescence of Non-Coalescent Cold and Hot Pure Liquid
- Molecular Description of the Surface Tension of Curved Interfaces
- The Effect of Surfactants on Marangoni Convection in the Isobutanol/Water System
- Generalized Separation of Variables in Nonlinear Heat and Mass Transfer Equations
- Chaos and Hyperchaos in a Model of the Belousov-Zhabotinsky Reaction in a Batch Reactor
- Anomalous Damping of Capillary Waves With Surfactant Solutions
- A New Discrete Model for the Non-Isothermic Dynamics of the Exothermic CO-Oxidation on Palladium Supported Catalyst
- Foam Microgeometry
- Instabilities By Local Heating Below an Interface
- Oscillatory Instability and High-Frequency Wave Modes in a Marangoni-Bénard Layer with Deformable Free Surface
