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A note on the existence of global solutions for reaction-diffusion equations with almost-monotonic nonlinearities

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  • We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in $L^q(\Omega)$ for each $1\leq q < \infty$. In particular, we do not assume restriction on the growth of the nonlinearites required by the standar local existence theory.
    Mathematics Subject Classification: Primary: 35A01, 35B33, 35D35, 35K57, 35K20; Secondary: 35B40, 35B41.


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