Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 30, No 1, (2019), 7p-20p
The local and global existence of the Cauchy problem for semilinear heat equations with small data is studied in the weighted L^∞(R^n ) framework by a simple contraction argument. The contraction argument is based on a weighted uniform control of solutions related with the free solutions and the first iterations for the initial data of negative power. 2010 Mathematics Subject Classification: 35K55, 35A01.