Geodesic
Mixed value problem for a nonlinear differential equation of fourth order with small parameter on the parabolic operator
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1703-1711

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We study the solvability of mixed value problem for one type of nonlinear partial differential equation, consisting superposition of parabolic and hyperbolic operators. By the method of separation variables we obtain the countable system of nonlinear integral equation. We use the method of successive approximations. It will be proved the convergence of obtained series. We study the continuously dependence of solution from small parameter. 
@article{ZVMMF_2011_51_9_a10,
     author = {T. K. Yuldashev},
     title = {Mixed value problem for a~nonlinear differential equation of fourth order with small parameter on the parabolic operator},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1703--1711},
     publisher = {mathdoc},
     volume = {51},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a10/}
}
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T. K. Yuldashev. Mixed value problem for a nonlinear differential equation of fourth order with small parameter on the parabolic operator. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1703-1711. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a10/