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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 2 (September 2020)   > Article

Global Small data Solutions for a system of semilinear heat equations and the corresponding system of damped wave equations with nonlinear memory

Solutions globales pour un système d’équations de chaleur semi-linéaires et système correspondant d’équations d’ondes amorties

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Mohamed Berbiche
University of Biskra
Algeria

Messaouda Terchi
University of Biskra
Algeria



Published on 3 September 2020   DOI : 10.21494/ISTE.OP.2020.0555

Abstract

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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



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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 2 (September 2020)   > Article