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One dimensional $p$-th power Newtonian fluid with temperature-dependent thermal conductivity
Reaction-Diffusion equations with spatially variable exponents and large diffusion
1. | Instituto de Matemática e Computaçã, Universidade Federal de Itajubá, 37500-903 Itajubá MG |
2. | Instituto de Matemática e Computação, Universidade Federal de Itajubá, 37500-903 - Itajubá - Minas Gerais, Brazil |
3. | Departamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, Paraná, Brazil |
References:
[1] |
H. Brézis, Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Publishing Company, Amsterdam, 1973. |
[2] |
H. Brézis, Analyse fonctionnelle:Théorie et applications, Masson, Paris, 1983. |
[3] |
A. N. Carvalho, Infinite dimensional dynamics described by ordinary differential equations, J. Differential Equation, 116 (1995), 338-404.
doi: 10.1006/jdeq.1995.1039. |
[4] |
A. N. Carvalho and J. K. Hale, Large diffusion with dispersion, Nonlinear Anal., 17 (1991), 1139-1151.
doi: 10.1016/0362-546X(91)90233-Q. |
[5] |
Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Math., 66 (2006), 1383-1406.
doi: 10.1137/050624522. |
[6] |
F. Ettwein and M. Růžička, Existence of local strong solutions for motions of electrorheological fluids in three dimensions, Comput. Math. Appl., 53 (2007), 595-604.
doi: 10.1016/j.camwa.2006.02.032. |
[7] |
E. Conway, D. Hoff and J. Smoller, Large time behavior of solutions of systems of non-linear reaction-diffusion equations, SIAM J. Appl. Math., 35 (1978), 1-16. |
[8] |
L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin, Heidelberg, 2011.
doi: 10.1007/978-3-642-18363-8. |
[9] |
X. L. Fan and Q. H. Zhang, Existence of solutions for $p(x)-$laplacian Dirichlet problems, Nonlinear Anal., 52 (2003), 1843-1852.
doi: 10.1016/S0362-546X(02)00150-5. |
[10] |
Z. Guo, Q. Liu, J. Sun and B. Wu, Reaction-diffusion systems with $p(x)-$growth for image denoising, Nonlinear Anal. Real World Appl., 12 (2011), 2904-2918.
doi: 10.1016/j.nonrwa.2011.04.015. |
[11] |
J. K. Hale, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. Appl., 118 (1986), 455-466.
doi: 10.1016/0022-247X(86)90273-8. |
[12] |
K. Rajagopal and M. Růžička, Mathematical modelling of electrorheological materials, Contin. Mech. Thermodyn., 13 (2001), 59-78. |
[13] |
M. Růžička, Flow of shear dependent electrorheological fluids, C. R. Acad. Sci. Paris S\'er. I., 329 (1999), 393-398.
doi: 10.1016/S0764-4442(00)88612-7. |
[14] |
M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory, in Lectures Notes in Mathematics (vol. 1748), Springer-Verlag, Berlin, 2000.
doi: 10.1007/BFb0104029. |
[15] |
J. Simsen, A global attractor for a $p(x)$-Laplacian inclusion, C. R. Acad. Sci. Paris Sér. I., 351 (2013), 87-90.
doi: 10.1016/j.crma.2013.02.009. |
[16] |
J. Simsen and C. B. Gentile, Well-posed $p$-laplacian problems with large diffusion, Nonlinear Anal., 71 (2009), 4609-4617.
doi: 10.1016/j.na.2009.03.041. |
[17] |
J. Simsen and M. S. Simsen, PDE and ODE limit problems for $p(x)$-Laplacian parabolic equations, J. Math. Anal. Appl., 383 (2011), 71-81.
doi: 10.1016/j.jmaa.2011.05.003. |
[18] |
J. Simsen, M. S. Simsen and M. R. T. Primo, Continuity of the flows and upper semicontinuity of global attractors for $p_s(x)$-Laplacian parabolic problems, J. Math. Anal. Appl., 398 (2013), 138-150.
doi: 10.1016/j.jmaa.2012.08.047. |
[19] |
J. Simsen, M. S. Simsen and M. R. T. Primo, On $p_s(x)$-Laplacian parabolic problems with non-globally Lipschitz forcing term, Z. Anal. Anwend., 33 (2014), 447-462.
doi: 10.4171/ZAA/1522. |
[20] |
J. Simsen, M. S. Simsen and F. B. Rocha, Existence of solutions for some classes of parabolic problems involving variable exponents, Nonlinear Stud., 21 (2014), 113-128. |
[21] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4684-0313-8. |
show all references
References:
[1] |
H. Brézis, Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Publishing Company, Amsterdam, 1973. |
[2] |
H. Brézis, Analyse fonctionnelle:Théorie et applications, Masson, Paris, 1983. |
[3] |
A. N. Carvalho, Infinite dimensional dynamics described by ordinary differential equations, J. Differential Equation, 116 (1995), 338-404.
doi: 10.1006/jdeq.1995.1039. |
[4] |
A. N. Carvalho and J. K. Hale, Large diffusion with dispersion, Nonlinear Anal., 17 (1991), 1139-1151.
doi: 10.1016/0362-546X(91)90233-Q. |
[5] |
Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Math., 66 (2006), 1383-1406.
doi: 10.1137/050624522. |
[6] |
F. Ettwein and M. Růžička, Existence of local strong solutions for motions of electrorheological fluids in three dimensions, Comput. Math. Appl., 53 (2007), 595-604.
doi: 10.1016/j.camwa.2006.02.032. |
[7] |
E. Conway, D. Hoff and J. Smoller, Large time behavior of solutions of systems of non-linear reaction-diffusion equations, SIAM J. Appl. Math., 35 (1978), 1-16. |
[8] |
L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin, Heidelberg, 2011.
doi: 10.1007/978-3-642-18363-8. |
[9] |
X. L. Fan and Q. H. Zhang, Existence of solutions for $p(x)-$laplacian Dirichlet problems, Nonlinear Anal., 52 (2003), 1843-1852.
doi: 10.1016/S0362-546X(02)00150-5. |
[10] |
Z. Guo, Q. Liu, J. Sun and B. Wu, Reaction-diffusion systems with $p(x)-$growth for image denoising, Nonlinear Anal. Real World Appl., 12 (2011), 2904-2918.
doi: 10.1016/j.nonrwa.2011.04.015. |
[11] |
J. K. Hale, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. Appl., 118 (1986), 455-466.
doi: 10.1016/0022-247X(86)90273-8. |
[12] |
K. Rajagopal and M. Růžička, Mathematical modelling of electrorheological materials, Contin. Mech. Thermodyn., 13 (2001), 59-78. |
[13] |
M. Růžička, Flow of shear dependent electrorheological fluids, C. R. Acad. Sci. Paris S\'er. I., 329 (1999), 393-398.
doi: 10.1016/S0764-4442(00)88612-7. |
[14] |
M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory, in Lectures Notes in Mathematics (vol. 1748), Springer-Verlag, Berlin, 2000.
doi: 10.1007/BFb0104029. |
[15] |
J. Simsen, A global attractor for a $p(x)$-Laplacian inclusion, C. R. Acad. Sci. Paris Sér. I., 351 (2013), 87-90.
doi: 10.1016/j.crma.2013.02.009. |
[16] |
J. Simsen and C. B. Gentile, Well-posed $p$-laplacian problems with large diffusion, Nonlinear Anal., 71 (2009), 4609-4617.
doi: 10.1016/j.na.2009.03.041. |
[17] |
J. Simsen and M. S. Simsen, PDE and ODE limit problems for $p(x)$-Laplacian parabolic equations, J. Math. Anal. Appl., 383 (2011), 71-81.
doi: 10.1016/j.jmaa.2011.05.003. |
[18] |
J. Simsen, M. S. Simsen and M. R. T. Primo, Continuity of the flows and upper semicontinuity of global attractors for $p_s(x)$-Laplacian parabolic problems, J. Math. Anal. Appl., 398 (2013), 138-150.
doi: 10.1016/j.jmaa.2012.08.047. |
[19] |
J. Simsen, M. S. Simsen and M. R. T. Primo, On $p_s(x)$-Laplacian parabolic problems with non-globally Lipschitz forcing term, Z. Anal. Anwend., 33 (2014), 447-462.
doi: 10.4171/ZAA/1522. |
[20] |
J. Simsen, M. S. Simsen and F. B. Rocha, Existence of solutions for some classes of parabolic problems involving variable exponents, Nonlinear Stud., 21 (2014), 113-128. |
[21] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4684-0313-8. |
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