Citation: |
[1] |
H. Amann, Global existence for semilinear parabolic problems, J. Reine Angew. Math., 360 (1985), 47-83.doi: 10.1515/crll.1985.360.47. |
[2] |
P. Baras and M. Pierre, Problèmes paraboliques semi-linéaires avec données mesures, (French, English summary), Applicable Analysis, 18 (1984), 111-149.doi: 10.1080/00036818408839514. |
[3] |
Ph. Bénilan, M. G. Crandall and A. Pazy, "Nonlinear Evolution Equations in Banach Spaces," preprint book. |
[4] |
M. Bisi, F. Confort and L. Desvillettes, Quasi-steady-state approximation for reaction-diffusion equations, Bull. Inst. Math., Acad. Sin. (N.S.), 2 (2007), 823-850. |
[5] |
D. Bothe, The instantaneous limit of a reaction-diffusion system, in "Evolution Equations and Their Applications in Physical and Life Sciences" (eds. G. Lumer, L. Weis), Marcel Dekker, Lect. Notes Pure Appl. Math., 215 (2000), 215-224. |
[6] |
D. Bothe, Instantaneous limits of reversible chemical reactions in presence of macroscopic convection, J. Differ. Equations, 193 (2003), 27-48.doi: 10.1016/S0022-0396(03)00148-7. |
[7] |
D. Bothe and D. Hilhorst, A reaction-diffusion system with fast reversible reaction, J. Math. Anal. Appl., 286 (2003), 125-135.doi: 10.1016/S0022-247X(03)00457-8. |
[8] |
D. Bothe, A. Lojewski and H.-J. Warnecke, Computational analysis of an instantaneous chemical reaction in a T-microreactor, AIChE J., 56 (2010), 1406-1415. |
[9] |
D. Bothe and M. Pierre, Quasi-steady-state approximation for a reaction-diffusion system with fast intermediate, J. Math. Anal. Appl., 368 (2010), 120-132.doi: 10.1016/j.jmaa.2010.02.044. |
[10] |
H. Brezis and W. A. Strauss, Semi-linear second-order elliptic equations in $L^1$, J. Math. Soc. Japan, 25 (1973), 565-590.doi: 10.2969/jmsj/02540565. |
[11] |
J. R. Cannon and C. D. Hill, On the movement of a chemical reaction interface, Indiana Univ. Math. J., 20 (1970), 429-453.doi: 10.1512/iumj.1970.20.20037. |
[12] |
J. R. Cannon and A. Fasano, Boundary value multidimensional problems in fast chemical reactions, Archive Rat. Mech. Anal., 53 (1973), 1-13.doi: 10.1007/BF00735697. |
[13] |
E. N. Dancer, D. Hilhorst, M. Mimura and L. A. Peletier, Spatial segregation limit of a competition-diffusion system, European J. Appl. Math., 10 (1999), 97-115.doi: 10.1017/S0956792598003660. |
[14] |
L. Desvillettes, K. Fellner, M. Pierre and J. Vovelle, About global existence for quadratic systems of reaction-diffusion, Advanced Nonlinear Studies, 7 (2007), 491-511. |
[15] |
P. Erdi and J. Toth, "Mathematical Models of Chemical Reactions," Manchester Univ. Press, Manchester 1989. |
[16] |
L. C. Evans, A convergence theorem for a chemical diffusion-reaction system, Houston J. Math., 6 (1980), 259-267. |
[17] |
D. Hilhorst, M. Mimura and H. Ninomiya, Fast reaction limit of competition-diffusion systems, in "Handbook of Differential Equations" (eds. C. M. Dafermos and M. Pokorny), Elsevier, Evolution Equations 5 (2009). |
[18] |
A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems,'' Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser Verlag, Basel, 1995. |
[19] |
R. H. Martin and M. Pierre, Nonlinear reaction-diffusion systems, in "Nonlinear Equations in the Applied Sciences" (eds. W.F. Ames and C. Rogers), Acad. Press, New York, Math. Sci. Eng., 185 (1991). |
[20] |
M. Pierre, Weak solutions and supersolutions in $L^1$ for reaction-diffusion systems, J. Evol. Equ., 3 (2003), 153-168.doi: 10.1007/s000280300007. |
[21] |
M. Pierre and D. Schmitt, Blowup in reaction-diffusion systems with dissipation of mass, SIAM J. Math. Anal., 28 (1997), 259-269.doi: 10.1137/S0036141095295437. |
[22] |
M. Pierre and D. Schmitt, Blowup in reaction-diffusion systems with dissipation of mass, SIAM Rev., 42 (2000), 93-106 (electronic).doi: 10.1137/S0036144599359735. |
[23] |
Y. Tonegawa, On the regularity of a chemical reaction interface, Comm. PDEs, 23 (1998), 1181-1207. |
[24] |
J. L. Vazquez, "The Porous Medium Equation, Mathematical Theory," Clarendon-Press, Oxford University Press, Oxford, 2007. |