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 \((u_0, v_0)\).
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Received: October 25, 1996
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Acosta, G., Rossi, J. Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition. Z. angew. Math. Phys. 48, 711–724 (1997). https://doi.org/10.1007/s000330050060
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DOI: https://doi.org/10.1007/s000330050060