-
Previous Article
Hopf dances near the tips of Busse balloons
- DCDS-S Home
- This Issue
-
Next Article
Modelling phase transitions via Young measures
The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction
1. | Center of Smart Interfaces, Technical University Darmstadt, Petersenstr. 32, 64287 Darmstadt, Germany |
2. | ENS Cachan Bretagne, IRMAR, EUB, Campus de Ker Lann, 35170 Bruz, France |
References:
[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. |
show all references
References:
[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. |
[1] |
Marvin S. Müller. Approximation of the interface condition for stochastic Stefan-type problems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4317-4339. doi: 10.3934/dcdsb.2019121 |
[2] |
Congming Li, Eric S. Wright. Modeling chemical reactions in rivers: A three component reaction. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 377-384. doi: 10.3934/dcds.2001.7.373 |
[3] |
Jifa Jiang, Junping Shi. Dynamics of a reaction-diffusion system of autocatalytic chemical reaction. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 245-258. doi: 10.3934/dcds.2008.21.245 |
[4] |
Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reaction-diffusion patterns. Communications on Pure and Applied Analysis, 2012, 11 (1) : 189-207. doi: 10.3934/cpaa.2012.11.189 |
[5] |
Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reaction-diffusion equations. Kinetic and Related Models, 2010, 3 (3) : 427-444. doi: 10.3934/krm.2010.3.427 |
[6] |
Parker Childs, James P. Keener. Slow manifold reduction of a stochastic chemical reaction: Exploring Keizer's paradox. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1775-1794. doi: 10.3934/dcdsb.2012.17.1775 |
[7] |
Klemens Fellner, Wolfang Prager, Bao Q. Tang. The entropy method for reaction-diffusion systems without detailed balance: First order chemical reaction networks. Kinetic and Related Models, 2017, 10 (4) : 1055-1087. doi: 10.3934/krm.2017042 |
[8] |
Maya Mincheva, Gheorghe Craciun. Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1207-1226. doi: 10.3934/mbe.2013.10.1207 |
[9] |
Gheorghe Craciun, Jiaxin Jin, Casian Pantea, Adrian Tudorascu. Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1305-1335. doi: 10.3934/dcdsb.2020164 |
[10] |
Ross Cressman, Vlastimil Křivan. Using chemical reaction network theory to show stability of distributional dynamics in game theory. Journal of Dynamics and Games, 2021 doi: 10.3934/jdg.2021030 |
[11] |
Andrea Picco, Lamberto Rondoni. Boltzmann maps for networks of chemical reactions and the multi-stability problem. Networks and Heterogeneous Media, 2009, 4 (3) : 501-526. doi: 10.3934/nhm.2009.4.501 |
[12] |
Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631 |
[13] |
Elena Shchepakina, Olga Korotkova. Canard explosion in chemical and optical systems. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 495-512. doi: 10.3934/dcdsb.2013.18.495 |
[14] |
Xiaoyan Zhang, Yuxiang Zhang. Spatial dynamics of a reaction-diffusion cholera model with spatial heterogeneity. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2625-2640. doi: 10.3934/dcdsb.2018124 |
[15] |
Rebecca McKay, Theodore Kolokolnikov, Paul Muir. Interface oscillations in reaction-diffusion systems above the Hopf bifurcation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2523-2543. doi: 10.3934/dcdsb.2012.17.2523 |
[16] |
Arno F. Münster. Simulation of stationary chemical patterns and waves in ionic reactions. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 35-46. doi: 10.3934/dcdsb.2002.2.35 |
[17] |
Marzia Bisi, Maria Groppi, Giampiero Spiga. Flame structure from a kinetic model for chemical reactions. Kinetic and Related Models, 2010, 3 (1) : 17-34. doi: 10.3934/krm.2010.3.17 |
[18] |
Marzia Bisi, Giampiero Spiga. On a kinetic BGK model for slow chemical reactions. Kinetic and Related Models, 2011, 4 (1) : 153-167. doi: 10.3934/krm.2011.4.153 |
[19] |
Ying Han, Zhenyu Lu, Sheng Chen. A hybrid inconsistent sustainable chemical industry evaluation method. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1225-1239. doi: 10.3934/jimo.2018093 |
[20] |
Bogdan Kazmierczak, Zbigniew Peradzynski. Calcium waves with mechano-chemical couplings. Mathematical Biosciences & Engineering, 2013, 10 (3) : 743-759. doi: 10.3934/mbe.2013.10.743 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]