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This article is cited in 3 scientific papers (total in 3 papers)
Unique solvability of certain matrix partial differential equations
S. A. Lomov Moscow Power Engineering Institute
Abstract:
A class of matrix-valued functions is picked out, invariant relative to the operator $\mathscr L\sum_{i=1}^n\lambda_i(x)\frac\partial{\partial t_i}-A(x)$, where $t=(t_1,\dots,t_n)$ are complex variables, $x$ is a real parameter, $A(x)$ is a matrix, $\{\lambda_i(x)\}_1^n=\sigma(A(x))$. It is shown that the operator $\mathscr L$ is normally solvable in the class picked out and a uniqueness theorem is proved for the solution of a nonstandard problem: the desired matrix-valued function $Z(x,t)$ is known only at a point and $\partial Z/\partial x\perp\operatorname{Ker}\mathscr L^*$. Such problems arise naturally when developing the general theory of singular perturbations.
Received: 03.05.1976
Citation:
S. A. Lomov, “Unique solvability of certain matrix partial differential equations”, Mat. Zametki, 21:4 (1977), 525–530; Math. Notes, 21:4 (1977), 293–296
Linking options:
https://www.mathnet.ru/eng/mzm7981 https://www.mathnet.ru/eng/mzm/v21/i4/p525
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Abstract page: | 216 | Full-text PDF : | 119 | First page: | 1 |
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