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Existence and boundary stabilization of solutions for the coupled semilinear system. (English) Zbl 1172.35360
Summary: We investigate the global existence of both strong and weak solutions for a semilinear coupled system with homogeneous feedback boundary conditions in bounded open domain \(\varOmega \) in \(\mathbb R^n\) with \(n\in \mathbb N\). We also prove the exponential decay of total energy associated with weak solutions.

MSC:
35G05 Linear higher-order PDEs
35N10 Overdetermined systems of PDEs with variable coefficients
35S15 Boundary value problems for PDEs with pseudodifferential operators
93D15 Stabilization of systems by feedback
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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