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We study the solution of the homogeneous advection-diffusion equation with a linear decay term, and several particular cases in which one or more of the decay, advection or diffusion processes is absent. A brief review is given of the classical Laplace and Fourier transform techniques for some of the particular cases. In order to solve the differential equation, the similarity transform method is extended by means of a conjecture which is readily proved, and which generates a “generalized similarity transform method”. The proposed method provides a means to obtain the similarity variables which reduce the problem to an ordinary differential equation with a known solution, and that completes the obtention of the analytical solution. Key-words: similarity transform; diffusion-advection equation; differential equations.

Obtenção de uma Solução Analítica da Equação de Difusão-Advecção com Decaimento de 1ª Ordem pelo Método da Transformação de Similaridade Generalizada