Well-posedness and qualitative behaviour of a semi-linear parabolic Cauchy problem arising from a generic model for fractional-order autocatalysis.

In this paper, we examine a semi-linear parabolic Cauchy problem with non-Lipschitz nonlinearity which arises as a generic form in a significant number of applications. Specifically, we obtain a well-posedness result and examine the qualitative structure of the solution in detail. The standard classical approach to establishing well-posedness is precluded owing to the lack of Lipschitz continuity for the nonlinearity. Here, existence and uniqueness of solutions is established via the recently developed generic approach to this class of problem (Meyer & Needham 2015 The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations. London Mathematical Society Lecture Note Series, vol. 419) which examines the difference of the maximal and minimal solutions to the problem. From this uniqueness result, the approach of Meyer & Needham allows for development of a comparison result which is then used to exhibit global continuous dependence of solutions to the problem on a suitable initial dataset. The comparison and continuous dependence results obtained here are novel to this class of problem. This class of problem arises specifically in the study of a one-step autocatalytic reaction, which is schematically given by A→B at rate apbq (where a and b are the concentrations of A and B, respectively, with 0

Haematology of the Australian sea lion, Neophoca cinerea.

The haematology of the Australian sea lion Neophoca cinerea was studied in a breeding colony on Kangaroo Island, South Australia. The methods used to catch and restrain the animals are described and the haematology of 38 animals of varying age and sex groups is recorded. Total values for both erythrocytes and leucocytes were similar to those of other marine mammals and were in the ranges of 4.77 to 6.08 X 10(6) mm3 and 6.3 to 14.6 X 10(3) mm3, respectively. Erythrocytes volumes were very large, measuring from 96 to 112 mm.3 The packed cell volumes ranged from 48.3 to 64.2% and the haemoglobin values from 16.2 to 21 gm percent. The neutrophil lymphocyte ratio varied from 0.5 to 6.2 and in some animals absolute lymphocyte values were less than 1,200 mm.3 In many animals the percentage of eosinophils was greater than 20%, suggesting parasitic disease.

Plasma biochemical values of clinically-normal Australian sea lions (Neophoca cinerea).

Seventeen biochemical constituents were assayed in the blood plasma of clinically-normal Australian sea lions (Neophoca cinerea). The sea lions formed part of a breeding colony which inhabits the southern coast of Kangaroo Island, South Australia. Little variation was found in any of the values obtained from animals of different age and sex. The results were compared with values published for California sea lions (Zalophus californianus), Northern fur seals (Callorhinus ursinus), Harbor seals (Phoca vitulina) and Northern elephant seals (Mirounga angustirostris).