Instantaneous shrinking in nonlinear diffusionconvection
Gilding, B.H. and Kersner, R. (1990) Instantaneous shrinking in nonlinear diffusionconvection. Proceedings of the American Mathematical Society, 109 (2). pp. 385394. ISSN 00029939

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Abstract:  The Cauchy problem for a nonlinear diffusionconvection equation is studied. The equation may be classified as being of degenerate parabolic type with one spatial derivative and a time derivative. It is shown that under certain conditions solutions of the initialvalue problem exhibit instantaneous shrinking. This is to say, at any positive time the spatial support of the solution is bounded above, although the support of the initial data function is not. This is a phenomenon which is normally only associated with nonlinear diffusion with strong absorption. In conjunction, a previously unreported phenomenon is revealed. It is shown that for a certain class of initial data functions there is a critical positive time such that the support of the solution is unbounded above at any earlier time, whilst the opposite is the case at any later time. 
Item Type:  Article 
Copyright:  © 1990 American Mathematical Society 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Link to this item:  http://purl.utwente.nl/publications/74997 
Official URL:  http://dx.doi.org/10.1090/S00029939199010074969 
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