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

Benaissa, Abbes; Miloudi, Mostefa; Mokhtari, Mokhtar

Commentat. Math. Univ. Carol. 56, No. 2, 169-186 (2015).

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.

Reviewer: Marie Kopáčková (Praha)

MSC:

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

Keywords:

Bresse system; delay term; exponential decay; initial boundary value problem; multiplier method; semigroup