Well‐Posedness and Long Time Behavior for an Abstract Coupled System of Kirchhoff and Heat Equations

ABSTRACT In this article, we consider a Cauchy problem in a Hilbert space an abstract quasilinear coupled system consisting of Kirchhoff and heat equations, where the coupling is an operator depending on a parameter . We establish the well‐posedness of solutions to the system by combining the Yosida approximation and the multiplier method. Furthermore, an explicit and case‐wise study of the behavior is presented depending on the parameter , based on the Lyapunov functional.