Rodríguez Bernal, AníbalTajdine, Anas2023-06-202023-06-202000-10-01Amann H., Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in: Function Spaces, Differential Operators and Nonlinear Analysis, Schmeisser, Triebel (Eds.), Teubner Texte zur Mathematik, 133, 1993, pp. 9–126. Arrieta J., Carvalho A., Rodríguez-Bernal A., Critical exponents at the boundary, C. R. Acad. Sci., Série I 327 (1998) 353–358. Arrieta J., Carvalho A.N., Rodríguez-Bernal A., Parabolic problems with nonlinear boundary conditions and critical nonlinearities, J. Differ. Eq. 165 (1999) 376–406. Arrieta J., Carvalho A.N., Rodríguez-Bernal A., Attractors of parabolic problems with nonlinear boundary conditions. Uniform bounds, Commun. Partial Differ. Eq. 25 (1–2) (2000) 1–37. Carvalho A.N., Oliva S.M., Pereira A.L., Rodríguez-Bernal A., Attractors for the parabolic problems with nonlinear boundary conditions, J. Math. Anal. and Appl. 207 (2) (1997) 409–461. Chipot M., Fila M., Quittner P., Stationary solution, blow-up and convergence to stationary solution for semilinear parabolic equations with nonlinear boundary conditions, Acta Math. U. Comenian. 60 (1991) 35–103. Hale J.K., Asymptotic Behavior of Dissipative System, Math. Surveys and Monogr. 25, Amer. Math. Soc., 1988. Rodríguez-Bernal A., Tajdine A., Nonlinear balance for reaction-diffusion equations under nonlinear boundary conditions: dissipativity and blow-up, Preprint, Dept. Matemática Aplicada U. Complutense de Madrid, Preprint Series MA-UCM 1999–011; J. Differ. Eq. (to appear). Walter W., On the existence and nonexistence in the large of solution of parabolic differential equations with a nonlinear boundary conditions, SIAM J. Math. Anal. 6 (1) (1975) 85–90.0764-444210.1016/S0764-4442(00)01652-9https://hdl.handle.net/20.500.14352/57855In this Note we study the asymptotic behavior of reaction diffusion equations with nonlinear boundary conditions. We obtain balance conditions between the reaction term and the nonlinear flux term which imply boundedness of solutions or blow-up in finite time.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0764444200016529http://www.sciencedirect.com/restricted access517.98Análisis funcional y teoría de operadores