
Previous Article
A generalization of the BlaschkeLebesgue problem to a kind of convex domains
 DCDSB Home
 This Issue

Next Article
Schauder estimates for singular parabolic and elliptic equations of Keldysh type
Nonexistence and short time asymptotic behavior of sourcetype solution for porous medium equation with convection in onedimension
1.  Institute of Applied Mathematics, Putian University, Putian 351100, China 
References:
[1] 
G. I. Barenblatt, On some unsteady motions of a liquid and gas in a porous medium, Prikladnaja Mathematika Mechanika, 16 (1952), 6778. 
[2] 
S. Kamm, Sourcetype solution for equation of nonstationary filtration, J. Math. Anal. Appl., 64 (1978), 263276. doi: 10.1016/0022247X(78)900367. 
[3] 
H. Brezis and A. Friedman, Nonlinear parabolic equations involving measure as initial conditions, J. Math. Pure. Appl., 62 (1983), 7397. 
[4] 
S. Kamin and L. A. Peletier, Sourcetype solution of generate diffusive equation with absorption, Israel. J. Math., 50 (1985), 219230. doi: 10.1007/BF02761403. 
[5] 
J. Zhao, Sourcetype solutions of degenrate quasilinear parabolic equations, J. of Dff. Eq., 92 (1991), 179198. doi: 10.1016/00220396(91)90046C. 
[6] 
T.P. Liu and M. Pierre, Sourcesolution and asymptotic behavior in conservation laws, J. of Diff. Eq., 51 (1984), 419441. doi: 10.1016/00220396(84)900962. 
[7] 
M. Escobedo, J. L. Vazquez and E. Zuazua, Asymptotic behavior and sourcetype solutions for a diffusionconvection equation, Arch. Rational Mech. Anal., 124 (1993), 4365. doi: 10.1007/BF00392203. 
[8] 
G. Lu, SourceType Solutions of Diffusion Equations with Nonlinear Convection, China J. of Contemporary Math., 28 (2000), 185188. 
[9] 
G. Lu, Explicit and similarity solutions for certain nonlinear parabolic diffusionconvection equations, J. Sys. Sci and Math. Scis., 22 (2002), 210222. 
[10] 
G. Lu and H. Yin, Sourcetype solutions of heat equation with convection in several variables spaces, Science in China, Series A, 54 (2011), 11451173. doi: 10.1007/s1142501142194. 
[11] 
G. Lu, Sourcetype solutions of nonlinear fokkerplanck equation of onedimension, Science China Mathemathics, 56 (2013), 18451868. doi: 10.1007/s1142501346122. 
[12] 
J. L. Vazquez, Perspectives in nonlinear diffusion: Between analysis, physics and geometry, International Congress of Mathematicians, Eur. Math. Soc., 1 (2007), 609634. doi: 10.4171/0221/23. 
[13] 
Y. Chen, Hölder estimates for solutions of uniformly degenerate parabolic equations, Chin Ann. of Math., 5B (1984), 661678. 
[14] 
G. Lu, A remark on $C^k$regularity of free boundary for porous medium equation with gravity term in onedimension, Appl. Math. A Journal of Chinese University, 7 (1992), 579593. (In Chinese) 
[15] 
O. A. Ladyzhenskaja, N. A. Solonnikov and N. N. Uralezeva, Linear and Quasilinear Equations of Parabolic Type, Trans. Math. Mono., 23, AMS Providence, R. I., 1968. 
[16] 
S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR. Sb., 81 (1970), 228255. 
[17] 
V. S. Varadarajan, Measure on topological spaces, Amer. Math. Soci. Trans., Series. 2 (1965), p48. 
[18] 
R. J. LeVeque, Finite Volue Methods for Hyperbolic Problems, Cambridge University Press, 2002. doi: 10.1017/CBO9780511791253. 
[19] 
P. J. Vila, An analysis of a class of secondorder accurate godunovtype schemes, SIAM Journal on Numerical Analysis, 26 (1989), 830853. doi: 10.1137/0726046. 
[20] 
T. Ding and C. Li, Ordinary differential equations, China Hihgher Education Press, Beijing, 1991. (In Chinease). 
show all references
References:
[1] 
G. I. Barenblatt, On some unsteady motions of a liquid and gas in a porous medium, Prikladnaja Mathematika Mechanika, 16 (1952), 6778. 
[2] 
S. Kamm, Sourcetype solution for equation of nonstationary filtration, J. Math. Anal. Appl., 64 (1978), 263276. doi: 10.1016/0022247X(78)900367. 
[3] 
H. Brezis and A. Friedman, Nonlinear parabolic equations involving measure as initial conditions, J. Math. Pure. Appl., 62 (1983), 7397. 
[4] 
S. Kamin and L. A. Peletier, Sourcetype solution of generate diffusive equation with absorption, Israel. J. Math., 50 (1985), 219230. doi: 10.1007/BF02761403. 
[5] 
J. Zhao, Sourcetype solutions of degenrate quasilinear parabolic equations, J. of Dff. Eq., 92 (1991), 179198. doi: 10.1016/00220396(91)90046C. 
[6] 
T.P. Liu and M. Pierre, Sourcesolution and asymptotic behavior in conservation laws, J. of Diff. Eq., 51 (1984), 419441. doi: 10.1016/00220396(84)900962. 
[7] 
M. Escobedo, J. L. Vazquez and E. Zuazua, Asymptotic behavior and sourcetype solutions for a diffusionconvection equation, Arch. Rational Mech. Anal., 124 (1993), 4365. doi: 10.1007/BF00392203. 
[8] 
G. Lu, SourceType Solutions of Diffusion Equations with Nonlinear Convection, China J. of Contemporary Math., 28 (2000), 185188. 
[9] 
G. Lu, Explicit and similarity solutions for certain nonlinear parabolic diffusionconvection equations, J. Sys. Sci and Math. Scis., 22 (2002), 210222. 
[10] 
G. Lu and H. Yin, Sourcetype solutions of heat equation with convection in several variables spaces, Science in China, Series A, 54 (2011), 11451173. doi: 10.1007/s1142501142194. 
[11] 
G. Lu, Sourcetype solutions of nonlinear fokkerplanck equation of onedimension, Science China Mathemathics, 56 (2013), 18451868. doi: 10.1007/s1142501346122. 
[12] 
J. L. Vazquez, Perspectives in nonlinear diffusion: Between analysis, physics and geometry, International Congress of Mathematicians, Eur. Math. Soc., 1 (2007), 609634. doi: 10.4171/0221/23. 
[13] 
Y. Chen, Hölder estimates for solutions of uniformly degenerate parabolic equations, Chin Ann. of Math., 5B (1984), 661678. 
[14] 
G. Lu, A remark on $C^k$regularity of free boundary for porous medium equation with gravity term in onedimension, Appl. Math. A Journal of Chinese University, 7 (1992), 579593. (In Chinese) 
[15] 
O. A. Ladyzhenskaja, N. A. Solonnikov and N. N. Uralezeva, Linear and Quasilinear Equations of Parabolic Type, Trans. Math. Mono., 23, AMS Providence, R. I., 1968. 
[16] 
S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR. Sb., 81 (1970), 228255. 
[17] 
V. S. Varadarajan, Measure on topological spaces, Amer. Math. Soci. Trans., Series. 2 (1965), p48. 
[18] 
R. J. LeVeque, Finite Volue Methods for Hyperbolic Problems, Cambridge University Press, 2002. doi: 10.1017/CBO9780511791253. 
[19] 
P. J. Vila, An analysis of a class of secondorder accurate godunovtype schemes, SIAM Journal on Numerical Analysis, 26 (1989), 830853. doi: 10.1137/0726046. 
[20] 
T. Ding and C. Li, Ordinary differential equations, China Hihgher Education Press, Beijing, 1991. (In Chinease). 
[1] 
Ansgar Jüngel, Ingrid Violet. Mixed entropy estimates for the porousmedium equation with convection. Discrete and Continuous Dynamical Systems  B, 2009, 12 (4) : 783796. doi: 10.3934/dcdsb.2009.12.783 
[2] 
Sofía Nieto, Guillermo Reyes. Asymptotic behavior of the solutions of the inhomogeneous Porous Medium Equation with critical vanishing density. Communications on Pure and Applied Analysis, 2013, 12 (2) : 11231139. doi: 10.3934/cpaa.2013.12.1123 
[3] 
Hongwei Zhang, Qingying Hu. Asymptotic behavior and nonexistence of wave equation with nonlinear boundary condition. Communications on Pure and Applied Analysis, 2005, 4 (4) : 861869. doi: 10.3934/cpaa.2005.4.861 
[4] 
Kaouther Ammar, Philippe Souplet. Liouvilletype theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 665689. doi: 10.3934/dcds.2010.26.665 
[5] 
Cong He, Hongjun Yu. Large time behavior of the solution to the Landau Equation with specular reflective boundary condition. Kinetic and Related Models, 2013, 6 (3) : 601623. doi: 10.3934/krm.2013.6.601 
[6] 
Luis Caffarelli, JuanLuis Vázquez. Asymptotic behaviour of a porous medium equation with fractional diffusion. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 13931404. doi: 10.3934/dcds.2011.29.1393 
[7] 
Belkacem SaidHouari, Radouane Rahali. Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III. Evolution Equations and Control Theory, 2013, 2 (2) : 423440. doi: 10.3934/eect.2013.2.423 
[8] 
Bhargav Kumar Kakumani, Suman Kumar Tumuluri. Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions. Discrete and Continuous Dynamical Systems  B, 2017, 22 (2) : 407419. doi: 10.3934/dcdsb.2017019 
[9] 
Gabriele Grillo, Matteo Muratori, Fabio Punzo. On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 59275962. doi: 10.3934/dcds.2015.35.5927 
[10] 
Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure and Applied Analysis, 2021, 20 (3) : 12131227. doi: 10.3934/cpaa.2021017 
[11] 
Bernard Brighi, S. Guesmia. Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain. Conference Publications, 2007, 2007 (Special) : 160169. doi: 10.3934/proc.2007.2007.160 
[12] 
P. ÁlvarezCaudevilla, J. D. Evans, V. A. Galaktionov. The Cauchy problem for a tenthorder thin film equation II. Oscillatory sourcetype and fundamental similarity solutions. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 807827. doi: 10.3934/dcds.2015.35.807 
[13] 
Jie Zhao. Large time behavior of solution to quasilinear chemotaxis system with logistic source. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 17371755. doi: 10.3934/dcds.2020091 
[14] 
Jiapeng Huang, Chunhua Jin. Time periodic solution to a coupled chemotaxisfluid model with porous medium diffusion. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 54155439. doi: 10.3934/dcds.2020233 
[15] 
Zhijun Zhang. Optimal global asymptotic behavior of the solution to a singular mongeampère equation. Communications on Pure and Applied Analysis, 2020, 19 (2) : 11291145. doi: 10.3934/cpaa.2020053 
[16] 
JeanClaude Saut, JunIchi Segata. Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 219239. doi: 10.3934/dcds.2019009 
[17] 
Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation. Discrete and Continuous Dynamical Systems  B, 2003, 3 (3) : 401408. doi: 10.3934/dcdsb.2003.3.401 
[18] 
Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 9911001. doi: 10.3934/dcds.2009.25.991 
[19] 
Ling Mi. Asymptotic behavior for the unique positive solution to a singular elliptic problem. Communications on Pure and Applied Analysis, 2015, 14 (3) : 10531072. doi: 10.3934/cpaa.2015.14.1053 
[20] 
Tingting Liu, Qiaozhen Ma. Timedependent asymptotic behavior of the solution for plate equations with linear memory. Discrete and Continuous Dynamical Systems  B, 2018, 23 (10) : 45954616. doi: 10.3934/dcdsb.2018178 
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]