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

Commentationes Mathematicae Universitatis Carolinae

Volumn 41, Issue 4, 2000, Pages 693-718

  Arkhipova, A ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Boundary value problem; Nonlinear parabolic systems; Solvability

Indexed keywords

EID: 18144396805     PISSN: 00102628     EISSN: 12137243     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. 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
2. 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)
3. Struwe M On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv. 60 (1985), 558-581
4. Ladyzhenskaja O.A., Solonnikov V.A., Uraltseva N.N Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Society, Providence, 1968
5. Giaquinta M., Modica G Local existence for quasilinear parabolic systems under non-linear boundary conditions, Ann. Mat. Pura Appl. 149 (1987), 41-59
6. Da Prato G., Spazi Lp (Ω, δ) e loro proprieta, Annali di Matem. LXIX (1965), 383-392
7. 2,δ(Ω, δ)., Ann. Mat. Pura Appl. 73 (1966), ser.4, 55-102
8. Arkhipova A On the Neumann problem for nonlinear elliptic systems with quadratic non-linearity, St. Petersburg Math. J. 8 (1997), no. 5, 1-17; in Russian: Algebra & Analysis, St. Petersburg 8 (1996), no. 5
9. Giaquinta M Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Stud. 105, Princeton Univ. Press, Princeton, N.J., 1983
10. Nečas J., Šverák V On regularity of solutions of nonlinear parabolic systems, Ann. Scuola Norm. Sup. Pisa 18 ser. IV, F.1 (1991), 1-11