ISSN:
0044-2275
Keywords:
Key words. Parabolic systems, nonlinear boundary conditions, blow up, global existence.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract. We study the behavior of positive solutions of the system¶¶ $u_t=\rm {div}(a(u)\nabla u) + f(u,v) \qquad v_t=\rm {div}(b(v) \nabla v) + g(u,v)$ ¶ in $\Omega$ a bounded domain with the boundary conditions ${\partial u \over \partial \eta}=r(u,v)$ , ${\partial v \over \partial \eta}=s(u,v)$ on $\partial \Omega$ and the initial data $(u_0 , v_0)$ . We find conditions on the functions a,b,f,g,r,s that guarantee the global existence (or finite time blow-up) of positive solutions for every $(u_0, v_0)$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000330050060
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