Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order.

Autor: Mitropol'skii, Yu., Khoma, N., Khoma, S.
Zdroj: Ukrainian Mathematical Journal; Jul2000, Vol. 52 Issue 7, p1068-1074, 7p
Abstrakt: On the basis of the exact solution of the linear Dirichlet problem $$u_{tt} - u_{xx} = f\left( {x,t} \right)$$ , $$u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2\pi } \right) = 0,$$ $$0 \leqslant x \leqslant \pi ,{\text{ }}0 \leqslant t \leqslant 2\pi ,$$ we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation utt − uxx = f( x, t, u, ut). [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
Externí odkaz: