Robert Laister, James Robinson and Mikołaj Sierżęga, A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations, Journal Of Differential Equations 262 (10) 2017, p. 4979–4987.see in PBN
Robert Laister, James Robinson and Mikołaj Sierżęga, Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains, Comptes Rendus Mathematique 352 (7-8) 2014, p. 621–626.see in PBN