Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

Amina Benramdane, Nadia Mezouar, Fatna Bensaber, Salah Boulaaras () and Rashid Jan
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Amina Benramdane: Higher School of Management, Tlemcen 13000, Algeria
Nadia Mezouar: Faculty of Economies Sciences, Mascara University, Mascara 29000, Algeria
Fatna Bensaber: Statistic and Random Modelization Laboratory, Tlemcen 13000, Algeria
Salah Boulaaras: Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia
Rashid Jan: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, Kajang 43000, Selangor, Malaysia

Mathematics, 2023, vol. 11, issue 22, 1-13

Abstract: 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.

Keywords: blow-up; fractional boundary dissipation; logarithmic Lamé system; partial differential equations; mathematical operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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