Geodesic
Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations
Applications of Mathematics, Tome 35 (1990) no. 3, pp. 192-208
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In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation $U_{tt}+dU_t-\sigma(x,t,U_x)_x+aU=f(x,t,U_x,U_t,U)$ with the Dirichlet boundary conditions is proved. No "smallness" assumptions are made concerning the function $f$. The main idea of the proof relies on the compensated compactness theory.
In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation $U_{tt}+dU_t-\sigma(x,t,U_x)_x+aU=f(x,t,U_x,U_t,U)$ with the Dirichlet boundary conditions is proved. No "smallness" assumptions are made concerning the function $f$. The main idea of the proof relies on the compensated compactness theory.
DOI : 10.21136/AM.1990.104403
Classification : 35B10, 35L70, 35Q20, 47J25
Keywords: telegraph equation; compensated compactness; vanishing viscosity method 
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Feireisl, Eduard. Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations. Applications of Mathematics, Tome 35 (1990) no. 3, pp. 192-208. doi: 10.21136/AM.1990.104403

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