Abstract
The Cauchy problem for the equation\(\partial u/\partial t = \mathcal{L}_x u = j(x) (u''_x )\) with positive essentially infinite-dimensional functionalsj(x) is studied in a properly chosen Banach space of functions on an infinite-dimensional separable real Hilbert space.
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References
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Additional information
Kiev Polytechnic Institute, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 663–670, June, 1994.
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Bogdanskii, Y.V. Cauchy problem for an essentially infinite-dimensional parabolic equation with variable coefficients. Ukr Math J 46, 714–724 (1994). https://doi.org/10.1007/BF02658173
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DOI: https://doi.org/10.1007/BF02658173