Dynamics of Curved Fronts

Dynamics of Curved Fronts

1988, Pages 105-130
Dynamics of Curved Fronts

Study of the Diffusion Equation with Growth of the Quantity of Matter and its Application to a Biology Problem

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This chapter discusses the diffusion equation with growth of the quantity of matter and its application to a biology problem. To drive an equation, a diffusion equation is considered for greater simplicity in just two dimensions. It is supposed that besides diffusion, there is a growth of the quantity of matter whose rate around a given point at the given time depends on the density already present, and an expression is derived using this. The chapter discusses a biology problem to find the rate of propagation of the gene A in a territory populated by an arbitrary species where a dominant gene A is spread out over with a constant concentration. The individuals having character A, that is, belonging to the genotypes AA and Aa, are privileged in the struggle for survival over individuals not having this character.

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