Geodesic
On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 1, pp. 135-148

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We study a one-dimensional system of two parabolic loaded equations of special kind and one-dimensional composite-type systems of special kind. Both systems are considered with Cauchy data. We obtain sufficient conditions for the existence of solutions in the class of smooth bounded functions. The method of splitting on the differential level (the weak approximation method) is used in the proof.
Keywords: inverse problem, direct problem, loaded equation, weak approximation method, system of partial differential equations, composite-type system.
Mots-clés : parabolic equation 
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     author = {I. V. Frolenkov and G. V. Romanenko},
     title = {On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with {Cauchy} data},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {135--148},
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     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a13/}
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I. V. Frolenkov; G. V. Romanenko. On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 1, pp. 135-148. http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a13/