@ARTICLE{10.21494/ISTE.OP.2020.0555, TITLE={Global Small data Solutions for a system of semilinear heat equations and the corresponding system of damped wave equations with nonlinear memory}, AUTHOR={Mohamed Berbiche, Messaouda Terchi, }, JOURNAL={Advances in Pure and Applied Mathematics}, VOLUME={11}, NUMBER={Issue 2 (September 2020)}, YEAR={2020}, URL={https://openscience.fr/Global-Small-data-Solutions-for-a-system-of-semilinear-heat-equations-and-the}, DOI={10.21494/ISTE.OP.2020.0555}, ISSN={1869-6090}, ABSTRACT={We consider the Cauchy problem for a strongly coupled semi-linear heat equations with some kind of nonlinearity in multi-dimensional space ℝN. We see under some conditions on the exponents and on the dimension N, that the existence and uniqueness of time-global solutions for small data and their asymptotic behaviors are obtained. This observation will be applied to the corresponding system of the damped wave equations in low dimensional space.}}