Global existence and energy decay of solutions to a Bresse system with delay terms. (English) Zbl 1340.35198

The authors discuss the initial-boundary value problem for the dissipative Bresse system with past history in the region \((0,+\infty)\times (0,L)\) with Dirichlet boundary conditions. Using an argument combining semigroup theory with the energy estimate method, they prove the global existence of a weak solution to the problem in Sobolev spaces. Furthermore, the exponential stability of the associated energy, and then of the solution, is deduced using the multiplier method.


35L53 Initial-boundary value problems for second-order hyperbolic systems
35B40 Asymptotic behavior of solutions to PDEs
74D05 Linear constitutive equations for materials with memory
35L70 Second-order nonlinear hyperbolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35L51 Second-order hyperbolic systems
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