Geodesic
On the existence of the harmonic variational flow subject to the two-sided conditions
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 28, Tome 243 (1997), pp. 324-337 Cet article a éte moissonné depuis la source Math-Net.Ru

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We shall devote ourselves to a study of constructing the weak solutions to parabolic systems of the variational flow type associated with the quadratic functional with the initial and boundary data from a suitable Sobolev space, subject to the two-sided conditions. In order to do this, we shall present an approach made by extending Rothe's method which is useful for solving the Cauchy problem and the initial- boundary-value problems for many sorts of equations. 
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     author = {N. Kikuchi and J.-i. Haga},
     title = {On the existence of the harmonic variational flow subject to the two-sided conditions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {324--337},
     year = {1997},
     volume = {243},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_243_a16/}
}
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N. Kikuchi; J.-i. Haga. On the existence of the harmonic variational flow subject to the two-sided conditions. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 28, Tome 243 (1997), pp. 324-337. http://geodesic.mathdoc.fr/item/ZNSL_1997_243_a16/