Abstract
We discuss the solvability of the nonhomogeneous boundary-value problem for the semilinear equation of the vibrating string x tt (t, y) − Δx(t, y) + f(t, y, x(t, y)) = 0 in a bounded domain and a certain type of superlinear nonlinearity. To this end, we deduce new dual variational method. Next, we discuss the stability of solutions with respect to the boundary control and initial conditions.
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Nowakowski, A. Nonhomogeneos Boundary-Value Problem for Semilinear Hyperbolic Equation. Stability. J Dyn Control Syst 14, 537–558 (2008). https://doi.org/10.1007/s10883-008-9050-z
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DOI: https://doi.org/10.1007/s10883-008-9050-z