On global existence for semilinear parabolic systems

We present some results on global existence of classical solutions of certain semilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains with a smooth boundary, relaxing the usual monotonicity assumptions on the nonlinearities.

[1]  Herbert Amann,et al.  Global existence for semilinear parabolic systems. , 1985 .

[2]  B. Sleeman,et al.  Maximum principles and comparison theorems for semilinear parabolic systems and their applications , 1993, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[3]  Jian Zhang.  Boundedness and blow-up behavior for reaction-diffusion systems in a bounded domain , 1999 .

[4]  Roberto Conti,et al.  Non-linear differential equations , 1966 .

[5]  Joachim Escher,et al.  Global solutions for quasilinear parabolic problems , 2002 .

[6]  Robert H. Martin,et al.  Global existence and boundedness in reaction-diffusion systems , 1987 .

[7]  Joachim Escher,et al.  Global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions , 1989 .

[8]  D. Schmitt,et al.  Blowup in reaction-diffusion systems with dissipation of mass , 1997 .

[9]  J. Escher,et al.  Global solutions for quasilinear parabolic systems , 2004 .

[10]  N. Alaa,et al.  Global Existence for Reaction-Diffusion Systems with Mass Control and Critical Growth with Respect to the Gradient , 2001 .

[11]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[12]  A. Constantin.  Global existence of solutions for perturbed differential equations , 1995 .

[13]  M. Escobedo,et al.  A Maximum Principle for Semilinear Parabolic Systems and Applications , 2001 .

[14]  Herbert Amann,et al.  Dynamic theory of quasilinear parabolic systems , 1990 .