Mapping a general diffusion model with auxiliary conditions

Résumé

Abstract The current paper describes new transformations that determines all possible ways that the partial differential equation, u t = σ 2 x j u x x + g ( x , t ) u , becomes the heat transfer equation. Typically, the approach contains unknown functions of integration, which can be obtained by specific auxiliary equations. As an important result, fundamental solutions can be found analytically. The technique is systematic and avoids the need for computer algebra—demonstrating a potent relationship between theory and practice. This study contributes to analytical techniques by offering new pathways to overcome problem solving.

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