Analysis of a parabolic cross-diffusion population model without self-diffusion
نویسندگان
چکیده
منابع مشابه
Analysis of a Parabolic Cross-diffusion Population Model without Self-diffusion
The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to vanish. The last assumption complicates the analysis since these terms usually provide H estimates of the solutions. The existence proof is based on a pos...
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Abstract. The global existence of a non-negative weak solution to a multi-dimensional parabolic strongly coupled model for two competing species is proved. The main feature of the model is that the diffusion matrix is non-symmetric and generally not positive definite and that the non-diagonal matrix elements (the cross-diffusion terms) are allowed to be “large”. The ideas of the existence proof...
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where j = i and gi(u1, u2) := (μi − γii ui − γij uj) ui. In the above, the given data is as follows: v is an environmental potential, c i ∈ R≥0, ai ∈ R>0 are diffusion coefficients, bi ∈ R are transport coefficients, μi ∈ R≥0 are the intrinsic growth rates, and γii ∈ R≥0 are intra-specific, whereas γij , i = j, ∈ R≥0 are interspecific competition coefficients. In addition to showing well-posedn...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2006
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.08.002