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Continua of local minimizers in a quasilinear model of phase transitions
A class of singular first order differential equations with applications in reaction-diffusion
1. | Area Departamental de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 1 - 1950-062 Lisboa, Portugal |
2. | Dipartimento di Matematica Pura ed Applicata, Univ. di Modena e Reggio Emilia, Via Campi, 213b, 41100 Modena, Italy |
3. | Faculdade de Ciências da Universidade de Lisboa, CMAF, Avenida Professor Gama Pinto 2, 1649-003 Lisboa, Portugal |
References:
[1] |
M. Arias, J. Campos and C. Marcelli, Fastness and continuous dependence in front propagation in Fisher-KPP equations, Discrete and Continuous Dynamical Systems Series B, 11 (2009), 11-30. |
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math., 30 (1978), 33-76.
doi: 10.1016/0001-8708(78)90130-5. |
[3] |
H. Berestycki and L. Nirenberg, Travelling fronts in cylinders, Annales de l'Institut Henri Poincare- Analyse non lineaire, 9 (1992), 497-572. |
[4] |
D. Bonheure and L. Sanchez, "Heteroclinic Orbits For Some Classes of Second and Fourth Order Differential Equations,'' Handbook of Differential Equations: Ordinary Differential Equations, Elsevier, 3 2006.
doi: 10.1016/S1874-5725(06)80006-4. |
[5] |
B. Gilding and R. Kersner, "Travelling Waves in Nonlinear Diffusion-Convection Reaction,'' Progress in Nonlinear Differential Equations and their Applications, 60. Birkhauser Verlag, Basel, 2004. |
[6] |
A. Hamydy, Travelling wave for absorption-convection-diffusion equations, Electronic Journal of Diff. Eq., 2006 (2006), 1-9. |
[7] |
A. Sánchez-Valdés and B. Hernández-Bermejo, New travelling wave solutions for the Fisher-KPP equation with general exponents, Appl. Math. Lett., 18 (2005), 1281-1285.
doi: 10.1016/j.aml.2005.02.016. |
[8] |
X. Hou, Y. Li and K. Meyer, Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities, Discrete and Contininuous Dynamical Systems, 26 (2010), 265-290. |
[9] |
A. Kolmogorov, I. Petrovski and N. Piscounov, Etude de l'équation de la diffusion avec croissance de la quantité de matiére et son application à un probléme biologique, Bull. Univ. Moskou Ser. Internat. Sec. A, 1 (1937), 1-25. |
[10] |
P. Maini, L. Malaguti, C. Marcelli and S. Matucci, Diffusion-aggregation processes with mono-stable reaction terms, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1175-1189.
doi: 10.3934/dcdsb.2006.6.1175. |
[11] |
P. Maini, L. Malaguti, C. Marcelli and S. Matucci, Aggregative movement and front propagation for bi-stable population models, Math. Models Methods Appl. Sci., 17 (2007), 1351-1368.
doi: 10.1142/S0218202507002303. |
[12] |
F. Sánchez-Garduño, P. Maini and J. Pérez-Velázquez, A non-linear degenerate equation for direct aggregation and traveling wave dynamics, Discrete and Continuous Dynamical Systems Series B, 13 (2010), 455-487. |
[13] |
F. Sánchez-Garduño and P. Maini, Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations, Journal of Mathematical Biology, 33 (1994), 163-192.
doi: 10.1007/BF00160178. |
[14] |
L. Malaguti and C. Marcelli, Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms, Math. Nachr., 242 (2002), 148-164.
doi: 10.1002/1522-2616(200207)242:1<148::AID-MANA148>3.0.CO;2-J. |
[15] |
L. Malaguti and C. Marcelli, Sharp Profiles in degenerate and doubly degenerate Fisher-KPP equations, Journal of Differential Equations, 195 (2003), 471-496.
doi: 10.1016/j.jde.2003.06.005. |
[16] |
P. Pang, Y. Wang and J. Yin, Periodic solutions for a class od reaction-diffusion equations with $p$-Laplacian, Nonlinear Analysis: Real World Applications, 11 (2010), 323-331.
doi: 10.1016/j.nonrwa.2008.11.006. |
show all references
References:
[1] |
M. Arias, J. Campos and C. Marcelli, Fastness and continuous dependence in front propagation in Fisher-KPP equations, Discrete and Continuous Dynamical Systems Series B, 11 (2009), 11-30. |
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math., 30 (1978), 33-76.
doi: 10.1016/0001-8708(78)90130-5. |
[3] |
H. Berestycki and L. Nirenberg, Travelling fronts in cylinders, Annales de l'Institut Henri Poincare- Analyse non lineaire, 9 (1992), 497-572. |
[4] |
D. Bonheure and L. Sanchez, "Heteroclinic Orbits For Some Classes of Second and Fourth Order Differential Equations,'' Handbook of Differential Equations: Ordinary Differential Equations, Elsevier, 3 2006.
doi: 10.1016/S1874-5725(06)80006-4. |
[5] |
B. Gilding and R. Kersner, "Travelling Waves in Nonlinear Diffusion-Convection Reaction,'' Progress in Nonlinear Differential Equations and their Applications, 60. Birkhauser Verlag, Basel, 2004. |
[6] |
A. Hamydy, Travelling wave for absorption-convection-diffusion equations, Electronic Journal of Diff. Eq., 2006 (2006), 1-9. |
[7] |
A. Sánchez-Valdés and B. Hernández-Bermejo, New travelling wave solutions for the Fisher-KPP equation with general exponents, Appl. Math. Lett., 18 (2005), 1281-1285.
doi: 10.1016/j.aml.2005.02.016. |
[8] |
X. Hou, Y. Li and K. Meyer, Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities, Discrete and Contininuous Dynamical Systems, 26 (2010), 265-290. |
[9] |
A. Kolmogorov, I. Petrovski and N. Piscounov, Etude de l'équation de la diffusion avec croissance de la quantité de matiére et son application à un probléme biologique, Bull. Univ. Moskou Ser. Internat. Sec. A, 1 (1937), 1-25. |
[10] |
P. Maini, L. Malaguti, C. Marcelli and S. Matucci, Diffusion-aggregation processes with mono-stable reaction terms, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1175-1189.
doi: 10.3934/dcdsb.2006.6.1175. |
[11] |
P. Maini, L. Malaguti, C. Marcelli and S. Matucci, Aggregative movement and front propagation for bi-stable population models, Math. Models Methods Appl. Sci., 17 (2007), 1351-1368.
doi: 10.1142/S0218202507002303. |
[12] |
F. Sánchez-Garduño, P. Maini and J. Pérez-Velázquez, A non-linear degenerate equation for direct aggregation and traveling wave dynamics, Discrete and Continuous Dynamical Systems Series B, 13 (2010), 455-487. |
[13] |
F. Sánchez-Garduño and P. Maini, Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations, Journal of Mathematical Biology, 33 (1994), 163-192.
doi: 10.1007/BF00160178. |
[14] |
L. Malaguti and C. Marcelli, Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms, Math. Nachr., 242 (2002), 148-164.
doi: 10.1002/1522-2616(200207)242:1<148::AID-MANA148>3.0.CO;2-J. |
[15] |
L. Malaguti and C. Marcelli, Sharp Profiles in degenerate and doubly degenerate Fisher-KPP equations, Journal of Differential Equations, 195 (2003), 471-496.
doi: 10.1016/j.jde.2003.06.005. |
[16] |
P. Pang, Y. Wang and J. Yin, Periodic solutions for a class od reaction-diffusion equations with $p$-Laplacian, Nonlinear Analysis: Real World Applications, 11 (2010), 323-331.
doi: 10.1016/j.nonrwa.2008.11.006. |
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