Solvability and stability of a semilinear wave equation with nonlinear boundary conditions |
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| Authors: | Andrzej Nowakowski |
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| Institution: | Faculty of Mathematics, University of Lodz, Banacha 22, 90-238 Lodz, Poland University of Humanity and Economics, Sterlinga 26, 90-360 Lodz, Poland |
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| Abstract: | We discuss solvability for the semilinear equation of the vibrating string xtt(t,y)−Δx(t,y)+f(t,y,x(t,y))=0 in a bounded domain, and certain type of nonlinearity on the boundary. To this effect we derive a new dual variational method. Next we discuss stability of solutions with respect to initial conditions. |
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| Keywords: | Semilinear equation of the vibrating string Nonlinearity on the boundary Dual variational method Stability of solutions |
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