On the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation
2021 ◽
Vol 104
(4)
◽
pp. 110-117
Keyword(s):
In this paper, by means of a change of variables, a nonlinear semi-periodic boundary value problem for the Goursat equation is reduced to a linear gravity problem for hyperbolic equations. Reintroducing a new function, the obtained problem is reduced to a family of boundary value problems for ordinary differential equations and functional relations. When solving a family of boundary value problems for ordinary differential equations, the parameterization method is used. The application of this approach made it possible to establish the coefficients of the unique solvability of the semi-periodic problem for the Goursat equation and to propose constructive algorithms for finding an approximate solution.
2021 ◽
Vol 73
(1)
◽
pp. 70-75
1995 ◽
Vol 18
(4)
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pp. 757-764
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2002 ◽
Vol 272
(1)
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pp. 67-78
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2000 ◽
Vol 101
(4)
◽
pp. 3365-3371
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2010 ◽
Vol 129
(1-2)
◽
pp. 166-181
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