GLOBAL EXISTENCE AND BLOW UP OF SOLUTION OF WAVE NONLINEAR EQUATION WITH BOUNDARY FRACTIONAL DAMPING AND LOGARITHMIC SOURCE TERMS - Mezouar N.; Boulaaras S.; Guefaifia R.; Jan R. (American Institute of Mathematical Sciences, 2025)
In this study, a global solution is presented for an initial boundary value problem involving a wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. The solution is obtained through the application of the energy method combined with the Faedo-Galarkin procedure. Additionally, a blow-up result for the solution is established, contingent upon the condition of non-positive initial energy. ? 2024 American Institute of Mathematical Sciences. All rights reserved.