TY - JOUR

T1 - Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic growth nonlinearities I. On the continuability of smooth solutions

AU - Arkhipova, A.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - A class of nonlinear parabolic systems with quadratic nonlinearities in the gradient (the case of two spatial variables) is considered. It is assumed that the elliptic operator of the system has a variational structure. The behavior of a smooth on a time interval [0, T) solution to the Cauchy-Neumann problem is studied. For the situation when the "local energies" of the solution are uniformly bounded on [0, T), smooth extendibility of the solution up to t = T is proved. In the case when [0, T) defines the maximal interval of the existence of a smooth solution, the singular set at the moment t = T is described.

AB - A class of nonlinear parabolic systems with quadratic nonlinearities in the gradient (the case of two spatial variables) is considered. It is assumed that the elliptic operator of the system has a variational structure. The behavior of a smooth on a time interval [0, T) solution to the Cauchy-Neumann problem is studied. For the situation when the "local energies" of the solution are uniformly bounded on [0, T), smooth extendibility of the solution up to t = T is proved. In the case when [0, T) defines the maximal interval of the existence of a smooth solution, the singular set at the moment t = T is described.

KW - Boundary value problem

KW - Nonlinear parabolic systems

KW - Solvability

UR - http://www.scopus.com/inward/record.url?scp=18144396805&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18144396805

VL - 41

SP - 693

EP - 718

JO - Commentationes Mathematicae Universitatis Carolinae

JF - Commentationes Mathematicae Universitatis Carolinae

SN - 0010-2628

IS - 4

ER -