Mathematics, Vol. 11, Pages 4591: Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

Mathematics, Vol. 11, Pages 4591: Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

Mathematics doi: 10.3390/math11224591

Authors: Amina Benramdane Nadia Mezouar Fatna Bensaber Salah Boulaaras Rashid Jan

In this work, by the use of a semigroup theory approach, we provide a global solution for an initial boundary value problem of the wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. In addition to this, we establish a blow-up result for the solution under the condition of non-positive initial energy.