Geodesic
On a construction of weak solutions to linear hyperbolic partial differential systems with the higher integrable gradients
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Tome 233 (1996), pp. 30-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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By taking linear hyperbolic partial differential equations as an illustration, we make a trial of constructing weak solutions, with the higher integrable gradients in the sense of Gehring, to hyperbolic differential equations with initial and boundary conditions. We adopt Rothe's method and follow the calculation which has been expanded by Giaquinta and Struwe in dealing with parabolic equations. To establish the scheme we evaluate some local estimates for solutions to Rothe's approximations to hyperbolic differential equations. Bibl. 6 titles. 
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     author = {K. Hoshino and N. Kikuchi},
     title = {On a~construction of weak solutions to linear hyperbolic partial differential systems with the higher integrable gradients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--52},
     year = {1996},
     volume = {233},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_233_a2/}
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K. Hoshino; N. Kikuchi. On a construction of weak solutions to linear hyperbolic partial differential systems with the higher integrable gradients. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Tome 233 (1996), pp. 30-52. http://geodesic.mathdoc.fr/item/ZNSL_1996_233_a2/