Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities II. Local and global solvability results

Commentationes Mathematicae Universitatis Carolinae

Volumn 42, Issue 1, 2001, Pages 53-76

  Arkhipova, A ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Boundary value problem; Nonlinear parabolic systems; Solvability

Indexed keywords

EID: 18144391121     PISSN: 00102628     EISSN: 12137243     Source Type: Journal    
DOI: None     Document Type: Article

References (9)

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3. Arkhipova A Global solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems with variational structure in the case of two spatial variables, Probl. Mat. Anal., No. 16, S.-Petersburg Univ., S.-Petersburg (1997), pp. 3-40; English transl.: J. Math. Sci. 92 (1998), no. 6, 4231-4255
4. Arkhipova A Local and global in time solvability of the Cauchy-Dirichlet problem to a class of nonlinear nondiagonal parabolic systems, Algebra & Analysis 11 (1999), no. 6, 81-119 (Russian)
5. Ladyzhenskaja O.A., Solonnikov V.A., Uraltseva N.N Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Society, Providence, 1968
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7. Struwe M Variationals Methods. Applications to Partial Differential Equations and Ha-miltonian Systems, Springer-Verlag, Berlin, 1990
8. Giaquinta M Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. of Math. Stud. 105, Princeton Univ. Press, Princeton, NJ, 1983
9. Arkhipova A Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic growth nonlinearities. I. On the continuability of smooth solutions, Comment. Math. Univ. Carolinae 41 (2000), no. 4, 693-718