@article { , title = {A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces}, abstract = {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 non-negative initial data u0∈Lq(Ω), when Ω⊂Rd is a bounded domain with Dirichlet boundary conditions. For q∈(1,∞) this holds if and only if limsups→∞s−(1+2q/d)f(s)}, doi = {10.1016/j.anihpc.2015.06.005}, issn = {0294-1449}, issue = {6}, journal = {Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire}, pages = {1519-1538}, publicationstatus = {Published}, publisher = {Elsevier}, url = {https://uwe-repository.worktribe.com/output/909531}, volume = {33}, keyword = {Research Group in Mathematics and its Applications, Semilinear heat equation, Dirichlet problem, Local existence, Non-existence, Instantaneous blow-up, Dirichlet heat kernel}, year = {2016}, author = {Laister, Robert and Robinson, James C. and Sierzega, Mikolaj and Vidal-Lopez, Alejandro} }