caa a22 4500 465756719 CHVBK 20180323111849.0 cr unu---uuuuu 170327e19901001xx s 000 0 eng 10.1007/BF00386242 doi (NATIONALLICENCE)springer-10.1007/BF00386242 An example of nonlinear toxic mass spreading [Elektronische Daten] [S. Shen, W. Perry] A one-dimensional, nonlinear problem of reproductive toxic mass spreading is studied in this paper. The nonlinearity is due to the difference of the reproduction rates in the toxic region and the nontoxic region. Multiple steady state solutions are found and their stability and instability are proved. Due to the instability, there may exist turning points (also called saddle-node bifurcation points), at which an infinitesimal perturbation of some parameters may cause a catastrophic change in the location of the steady state toxic front (the interface of the toxic region and the nontoxic region). For the time dependent case, the propagation of the toxic front is considered. An integral equation is derived to determine the propagation of the toxic front. Some numerical results are found for a specific example. Kluwer Academic Publishers, 1990 toxic mass spreading nationallicence stability nationallicence bifurcation nationallicence propagation of front nationallicence Shen S. Department of Mathematics and Climate System Research Program, College of Geosciences, USA aut Perry W. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA aut Applied Scientific Research Kluwer Academic Publishers 47/4(1990-10-01), 323-339 0003-6994 47:4<323 1990 47 10494 https://doi.org/10.1007/BF00386242 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00386242 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shen S. Department of Mathematics and Climate System Research Program, College of Geosciences, USA aut NATIONALLICENCE 700 1- Perry W. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA aut NATIONALLICENCE 773 0- Applied Scientific Research Kluwer Academic Publishers 47/4(1990-10-01), 323-339 0003-6994 47:4<323 1990 47 10494 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer