Geodesic
On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 41-57

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In this paper, we examine the solvability of a new class of nonclassical direct problems for multidimensional loaded parabolic equations with Cauchy data. We obtain sufficient conditions for the solvability of the problem; the proof is based on the method of weak approximation. By an example, we demonstrate the application of the theorem proved to the study of inverse problems for multidimensional parabolic equations with Cauchy data.
Mots-clés : parabolic equation
Keywords: loaded equation, Cauchy problem, solvability, method of weak approximation. 
@article{INTO_2018_156_a3,
     author = {I. V. Frolenkov and E. N. Kriger},
     title = {On the solvability of the {Cauchy} problem for a certain class of multidimensional loaded parabolic equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {41--57},
     publisher = {mathdoc},
     volume = {156},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_156_a3/}
}
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I. V. Frolenkov; E. N. Kriger. On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 41-57. http://geodesic.mathdoc.fr/item/INTO_2018_156_a3/