Geodesic
On uniqueness classes for degenerating parabolic equations
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 453-469

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We study the uniqueness classes of a generalized solution of the Cauchy problem \begin{equation} u_t=\frac12\sum_{i,j=1}^na_{ij}(x)u_{x_ix_j}+\sum_{i=1}^na_i(x)u_{x_i}\equiv Lu,\quad u(0,x)=\varphi(x),\quad x\in\mathbf R^n,\ t\in[0,T], \end{equation} when the matrix $\bigl\{a_{ij}(x)\bigr\}$ is degenerate. A generalized solution is introduced with the help of an infinitesimal operator of a Markov process connected with the operator in (1). In the proof of the theorems we use probabilistic characteristics of this process. Bibliography: 11 titles. 
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     author = {I. M. Sonin},
     title = {On uniqueness classes for degenerating parabolic equations},
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     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_4_a0/}
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I. M. Sonin. On uniqueness classes for degenerating parabolic equations. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 453-469. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a0/