Existence and nonexistence of solution of fractional Lam� wave equation with polynomial nonlinearity source terms

• Main Authors: Mezouar N., Boulaaras S., Jan R., Benramdane A., Bensaber F.
• Other Authors: 57193545019
• Format: Article
• Published: Elsevier B.V. 2024
• Subjects: Blow-up; Fractional differential equation; Global existence; Lam� system; Mathematical operators; Partial differential equations; Control nonlinearities; Group theory; Nonlinear equations; Polynomials; Wave equations; Existence and non existences; Existence of Solutions; Fractional differential equations; Lame system; Lame waves; Nonexistence of solutions; Polynomial nonlinearities; Source terms

In this work, we examine the existence and nonexistence of solution for lam� wave equation with a nonlinear source terms and fractional boundary dissipation. By using the semi group theory approach, we prove the existence of a global solution. Furthermore, we established the blow-up results under the non-positive initial energy condition. � 2023 The Author(s)