Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 2 (September 2020) > Article
Mohamed Berbiche
University of Biskra
Algeria
Messaouda Terchi
University of Biskra
Algeria
Published on 3 September 2020 DOI : 10.21494/ISTE.OP.2020.0555
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.
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.
Parabolic system damped wave system global existence critical exponent
Parabolic system damped wave system global existence critical exponent