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Explicit solutions are obtained for evolution equations for explosively unstable situations. These solutions include the effects of diffusion with linear or quadratic density dependence of the diffusion coefficient. As a result of balance between the diffusion and nonlinear terms, explosive growth in time can occur with a preservation in shape of certain spatial distributions. The solutions are generalized to cases of two interacting populations.
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H. Wilhelmsson (1987) studied this question.
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