Geodesic
Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities II. Local and global solvability results
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 53-76.

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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.
Classification : 35J65, 35K45, 35K50, 35K55, 35K60
Keywords: boundary value problem; nonlinear parabolic systems; solvability 
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     title = {Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities  {II.} {Local} and global solvability results},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {53--76},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2001},
     mrnumber = {1825372},
     zbl = {1115.35069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001__42_1_a3/}
}
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Arkhipova, A. Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities  II. Local and global solvability results. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 53-76. http://geodesic.mathdoc.fr/item/CMUC_2001__42_1_a3/