The equivalence problem for the heat equation
DOI10.1063/1.525261zbMath0508.35040OpenAlexW2058904898MaRDI QIDQ4746164
Publication date: 1982
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.525261
conservation lawsdifferential formscontact transformationequivalence criteriaEstabrook-Wahlquist methodprolongation forms
Heat equation (35K05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Differential forms in global analysis (58A10) Continuation and prolongation of solutions to PDEs (35B60) Second-order parabolic equations (35K10) Representations of solutions to partial differential equations (35C99)
Cites Work
- The Estabrook-Wahlquist method with examples of application
- An algorithm to construct evolution equations with a given set of conserved densities
- On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
- On the Transformation of Diffusion Processes into the Wiener Process
- Linearization of relativistic nonlinear wave equations
- Group Transformations and the Nonlinear Heat Diffusion Equation
- On the exactly solvable equation$S_t = [ ( \beta S + \gamma )^{ - 2} S_x _x + \alpha ( \beta S + \gamma )^{ - 2} S_x $ Occurring in Two-Phase Flow in Porous Media]
- Prolongation structures of nonlinear evolution equations
- Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
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