Abstract
We consider the existence and decay estimates of solutions for Kirchhoff type equation with damping logarithmic source term. We proved global existence of solutions under suitable conditons by potential well method and the decay estimates result of the solutions for subcritical energy level.
Highlights
Erhan Piskin and Nazlı Irkıl abstract: We consider the existence and decay estimates of solutions for Kirchhoff type equation with damping logarithmic source term
We proved global existence of solutions under suitable conditons by potential well method and the decay estimates result of the solutions for subcritical energy level
In 1876, Kirchhoff [3] introduced Kirchhoff type equation in order to study the nonlinear vibrations of an elastic string
Summary
In 1876, Kirchhoff [3] introduced Kirchhoff type equation in order to study the nonlinear vibrations of an elastic string. Kirchhoff model to described the transverse oscillations of stretched string, with local or nonlocal flexural rigidity [24]. Kirchhoff model was very important for many applications in mechanics, elastic theory and other areas of mathematical physics [3]. It is worth noting that there have been mang interesting study of the with initial and boundary value problems for Kirchhoff type equation, for details on Kirchhoff type equation, we refer to see the works [9,13,19,20,23]. |ux|2 ds uxx, where t > 0 and 0 < x < L. E is the Young modulus, p is the mass density, h is the cross-section area, P0 is the initial axial tension, δ is the resistance modulus, f is the external force
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