caa a22 4500 477077285 CHVBK 20180405111441.0 cr unu---uuuuu 170330e19960701xx s 000 0 eng 10.1007/BF00049247 doi (NATIONALLICENCE)springer-10.1007/BF00049247 Forbes Larry Department of Mathematics, University of Queensland, 4072, St. Lucia, Queensland, Australia aut Stationary circular target patterns in a surface burning reaction [Elektronische Daten] [Larry Forbes] A simple model for burning on the circular face of a substrate is analyzed. It is shown that spatial patterns can form, in which the temperature develops hot and cold regions arranged in concentric circular rings. A linearized study shows the parameter values for which small amplitude patterns are stable. The fully non-linear equations are then solved using an efficient shooting method in the spatial variable, and an extremely complicated bifurcation diagram is obtained, from which it follows that multiple solutions occur at the same values of the defining parameters. The effect of heat leakage at the edges of the circular region is considered, and complicated non-linear behaviour occurs in this case also. Seven different temperature patterns, all co-existing at the same parameter values, are presented in a particular instance. Kluwer Academic Publishers, 1996 Exothermic reaction nationallicence pattern formation nationallicence multiple solution nationallicence shooting method nationallicence bifurcation diagrams nationallicence Journal of Engineering Mathematics Kluwer Academic Publishers; http://www.wkap.nl 30/4(1996-07-01), 471-486 0022-0833 30:4<471 1996 30 10665 https://doi.org/10.1007/BF00049247 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049247 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Forbes Larry Department of Mathematics, University of Queensland, 4072, St. Lucia, Queensland, Australia aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers; http://www.wkap.nl 30/4(1996-07-01), 471-486 0022-0833 30:4<471 1996 30 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer