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Global and nonglobal existence for a strongly coupled parabolic system on a general domain
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We consider the parabolic system ut−Δu=f(t)urvs,vt−Δv=g(t)uqvs, in Ω×(0,T), where Ω⊂RN is either an unbounded or bounded domain and f,g∈C[0,∞). We find conditions for the global existence or nonglobal existence, which are expressed in terms of the behavior of ‖S(t)u0 as b4451e93a" title="Click to view the MathML source">t→∞, where u(t)=S(t)u0 is the solution of the linear problem ut−Δu=0,u(0)=u0.

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