Study of the classical solution to the one-dimensional mixed problem for a class of semilinear long-wave equations |
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Authors: | F M Namazov K I Khudaverdiyev |
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Institution: | 1.Faculty of Mechanics and Mathematics,Baku State University,Baku,Azerbaijan |
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Abstract: | Many problems in mathematical physics are reduced to one- or multidimensional initial and initial-boundary value problems
for, generally speaking, strongly nonlinear Sobolev-type equations. In this work, local and global classical solvability is
studied for the one-dimensional mixed problem with homogeneous Riquier-type boundary conditions for a class of semilinear
long-wave equations
$
U_{tt} \left( {t,x} \right) - U_{xx} \left( {t,x} \right) - \alpha U_{ttxx} \left( {t,x} \right) = F\left( {t,x,U\left( {t,x} \right),U_x \left( {t,x} \right),U_{xx} \left( {t,x} \right),U_t \left( {t,x} \right),U_{tx} \left( {t,x} \right),U_{txx} \left( {t,x} \right)} \right)
$
U_{tt} \left( {t,x} \right) - U_{xx} \left( {t,x} \right) - \alpha U_{ttxx} \left( {t,x} \right) = F\left( {t,x,U\left( {t,x} \right),U_x \left( {t,x} \right),U_{xx} \left( {t,x} \right),U_t \left( {t,x} \right),U_{tx} \left( {t,x} \right),U_{txx} \left( {t,x} \right)} \right)
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Keywords: | |
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