Geodesic
Краевые задачи для ультрапараболических и квазиультрапараболических уравнений с меняющимся направлением эволюции
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 56-63

Voir la notice de l'article provenant de la source Math-Net.Ru

We examine the solvability of the boundary-value problems for the differential equation \begin{gather*} h(t)u_t+(-1)^mD^{2m+1}_au-\Delta u+c(x,t,a)u=f(x,t,a); \\ x\in\Omega\subset \mathbb{R}^n, \quad 0, \quad 0, \quad D^k_a=\frac{\partial^k}{\partial a^k}, \end{gather*} where the sign of the function $h(t)$ arbitrarily alternates in the interval $[0,T]$. The existence and uniqueness theorems of regular (i.e., possessing all generalized derivatives in the Sobolev sense) solutions are proved.
Mots-clés : ultraparabolic equation, evolution
Keywords: nonclassical differential equation of odd order, boundary-value problem, regular solution, existence, uniqueness. 
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     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {56--63},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a6/}
}
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A. I. Kozhanov. Краевые задачи для ультрапараболических и квазиультрапараболических уравнений с меняющимся направлением эволюции. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 56-63. http://geodesic.mathdoc.fr/item/INTO_2018_149_a6/