American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 486-495. doi: 10.3934/proc.2009.2009.486

Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations

Hirotoshi Kuroda 1, and  Noriaki Yamazaki 2,

1. 

Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8,, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan
2. 

Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama, 221-8686, Japan

Received  July 2008 Revised  April 2009 Published  September 2009

We consider a vectorial nonlinear diffusion equation with inhomogeneous terms in one-dimensional space. In this paper we study approximating problems of singular diffusion equations with a piecewise constant initial data. Also we consider the relationship between the singular diffusion problem and its approximating ones. Moreover we give some numerical experiments for the approximating equation with inhomogeneous terms and a piecewise constant initial data.
Keywords: Approximating problems, numerical experiments, vectorial singular diffusion.
Mathematics Subject Classification: Primary: 35K55, 65M99; Secondary: 35R35.
Citation: Hirotoshi Kuroda, Noriaki Yamazaki. Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations. Conference Publications, 2009, 2009 (Special) : 486-495. doi: 10.3934/proc.2009.2009.486
[1]

G. Bellettini, Giorgio Fusco, Nicola Guglielmi. A concept of solution and numerical experiments for forward-backward diffusion equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 783-842. doi: 10.3934/dcds.2006.16.783
[2]

Joseph D. Fehribach. Using numerical experiments to discover theorems in differential equations. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 495-504. doi: 10.3934/dcdsb.2003.3.495
[3]

Z. Foroozandeh, Maria do rosário de Pinho, M. Shamsi. On numerical methods for singular optimal control problems: An application to an AUV problem. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2219-2235. doi: 10.3934/dcdsb.2019092
[4]

Gabriella Bretti, Maya Briani, Emiliano Cristiani. An easy-to-use algorithm for simulating traffic flow on networks: Numerical experiments. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 379-394. doi: 10.3934/dcdss.2014.7.379
[5]

Winfried Just. Approximating network dynamics: Some open problems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : 1917-1930. doi: 10.3934/dcdsb.2018188
[6]

Marco Campo, José R. Fernández, Maria Grazia Naso. A dynamic problem involving a coupled suspension bridge system: Numerical analysis and computational experiments. Evolution Equations & Control Theory, 2019, 8 (3) : 489-502. doi: 10.3934/eect.2019024
[7]

Gisella Croce, Nikos Katzourakis, Giovanni Pisante. $\mathcal{D}$-solutions to the system of vectorial Calculus of Variations in $L^∞$ via the singular value problem. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6165-6181. doi: 10.3934/dcds.2017266
[8]

Yan-Yu Chen, Yoshihito Kohsaka, Hirokazu Ninomiya. Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 697-714. doi: 10.3934/dcdsb.2014.19.697
[9]

Kin Ming Hui. Collasping behaviour of a singular diffusion equation. Discrete & Continuous Dynamical Systems - A, 2012, 32 (6) : 2165-2185. doi: 10.3934/dcds.2012.32.2165
[10]

Florian De Vuyst, Francesco Salvarani. Numerical simulations of degenerate transport problems. Kinetic & Related Models, 2014, 7 (3) : 463-476. doi: 10.3934/krm.2014.7.463
[11]

Paulo Cesar Carrião, R. Demarque, Olímpio H. Miyagaki. Nonlinear Biharmonic Problems with Singular Potentials. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2141-2154. doi: 10.3934/cpaa.2014.13.2141
[12]

Annamaria Canino, Luigi Montoro, Berardino Sciunzi. The jumping problem for nonlocal singular problems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6747-6760. doi: 10.3934/dcds.2019293
[13]

Eric Falcon. Laboratory experiments on wave turbulence. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 819-840. doi: 10.3934/dcdsb.2010.13.819
[14]

Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515
[15]

Mudassar Imran, Mohamed Ben-Romdhane, Ali R. Ansari, Helmi Temimi. Numerical study of an influenza epidemic dynamical model with diffusion. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020168
[16]

Kin Ming Hui, Sunghoon Kim. Existence of Neumann and singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4859-4887. doi: 10.3934/dcds.2015.35.4859
[17]

Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631
[18]

Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129
[19]

Qiaolin He. Numerical simulation and self-similar analysis of singular solutions of Prandtl equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 101-116. doi: 10.3934/dcdsb.2010.13.101
[20]

G. Machado, L. Trabucho. Analytical and numerical solutions for a class of optimization problems in elasticity. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1013-1032. doi: 10.3934/dcdsb.2004.4.1013

 Impact Factor: 

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences