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Variational approach to stability of semilinear wave equation with nonlinear boundary conditions

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  • We discuss solvability for the semilinear equation of the vibrating string $ x_{tt}(t,y)-\Delta x(t,y)=F_{x}(t,y,x(t,y))-G_{x}(t,y,x(t,y))$ in bounded domain and same type of nonlinearity on the boundary. To this effect we derive new variational methods one for the boundary equation the second for interior equation. Next we discuss stability of solutions with respect to initial conditions basing on variational approach.
    Mathematics Subject Classification: Primary: 35L05; Secondary: 35L20.

    Citation:

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