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A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces (2015)
Journal Article
Laister, R., Robinson, J. C., Sierzega, M., & Vidal-Lopez, A. (2016). A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 33(6), 1519-1538. https://doi.org/10.1016/j.anihpc.2015.06.005

We consider the scalar semilinear heat equation ut−Δu=f(u), where f:[0,∞)→[0,∞) is continuous and non-decreasing but need not be convex. We completely characterise those functions f for which the equation has a local solution bounded in Lq(Ω) for all... Read More about A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces.