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Existence of global solutions in time for reaction-diffusion systems with inhomogeneous terms in cones. (English) Zbl 1255.35133

Summary: We consider nonnegative solutions of the initial-boundary value problems in cone domains for the reaction-diffusion systems with inhomogeneous terms dependent on space-time coordinates. In this paper we show the condition for the existence of global solutions. Our conditions for the global existence are optimal in view of our nonexistence results in [the authors, J. Math. 33, No. 1, 131–145 (2009; Zbl 1180.35278)].

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35K58 Semilinear parabolic equations

Citations:

Zbl 1180.35278
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Full Text: Euclid