Geodesic
The infinite-dimensional Liouville equation
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 17-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem on the existence of a solution of the Cauchy problem is proved for the infinite-dimensional Liouville equation for the $\varphi^n(x)$ model of a scalar bosonic field and for the $\varphi^n(x(\sigma))$ model of a bosonic string field. The Liouville equation is regarded as an ordinary differential equation in a locally convex space of functions on an infinite-dimensional phase space. 
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A. Yu. Khrennikov. The infinite-dimensional Liouville equation. Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 17-41. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a1/

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