Petersson, Joakim H. On global existence for semilinear parabolic systems. (English) Zbl 1072.35084 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 60, No. 2, 337-347 (2005). This paper concerns global existence results for classical solutions of semilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains. The study is done under weak monotonicity requirements on the nonlinearities. Reviewer: Sebastian Anita (Iaşi) Cited in 6 Documents MSC: 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 35K55 Nonlinear parabolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:parabolic systems; global solutions; homogeneous Dirichlet boundary; weak monotonicity requirements PDF BibTeX XML Cite \textit{J. H. Petersson}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 60, No. 2, 337--347 (2005; Zbl 1072.35084) Full Text: DOI References: [1] Amann, H., Global existence for semilinear parabolic systems, J. reine angew. math., 360, 47-83, (1985) · Zbl 0564.35060 [2] Amann, H., Dynamic theory of quasilinear parabolic systems. III. global existence, Math. Z., 202, 219-250, (1989) · Zbl 0702.35125 [3] Alaa, N.; Mounir, I., Global existence for reaction – diffusion systems with mass control and critical growth with respect to the gradient, J. math. anal. appl., 253, 532-557, (2001) · Zbl 0963.35078 [4] Constantin, A., Some observations on a Conti’s result, Atti accad. naz. lincei rend. cl. sci. fis. mat. natur. ser. IX fasc. 2, II, 137-145, (1991) · Zbl 0732.34011 [5] Constantin, A., Global existence of solutions for perturbed differential equations, Annali mat. pura appl., 168, 237-299, (1995) [6] Constantin, A.; Escher, J., Global solutions for quasilinear parabolic problems, J. evolution equations, 2, 97-111, (2002) · Zbl 1004.35070 [7] Constantin, A.; Escher, J.; Yin, Z., Global solutions for quasilinear parabolic systems, J. differential equations, 197, 73-84, (2004) · Zbl 1043.35066 [8] Conti, R.; Sansone, G., Non-linear differential equations, (1964), Pergamon Press New York · Zbl 0128.08403 [9] Dickstein, F.; Escobedo, M., A maximum principle for semilinear parabolic systems and applications, Nonlinear anal., 45, 825-837, (2001) · Zbl 0986.35044 [10] Escher, J., Global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions, Math. ann., 284, 285-305, (1989) · Zbl 0652.35065 [11] Hollis, S.; Martin, R.; Pierre, M., Global existence and boundedness in reaction – diffusion systems, SIAM J. math. anal., 18, 744-761, (1987) · Zbl 0655.35045 [12] Lu, G.; Sleeman, B.D., Maximum principles and comparison theorems for semilinear parabolic systems and their applications, Proc. roy. soc. Edinburgh, 123, 857-885, (1993) · Zbl 0791.35006 [13] Pierre, M.; Schmidt, D., Blowup in reaction – diffusion systems with dissipation of mass, SIAM J. math. anal., 28, 259-269, (1997) · Zbl 0877.35061 [14] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Mathematics, vol. 1072, Springer, Berlin, 1984. · Zbl 0546.35003 [15] Zhang, J., Boundedness and blow-up behavior for reaction – diffusion systems in bounded domains, Nonlinear anal., 35, 833-844, (1999) · Zbl 0932.35125 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.