Cauchy problem for a sixth order CahnHilliard type equation with inertial term
Pages: 315  324,
Issue 3,
September
2015
doi:10.3934/eect.2015.4.315 Abstract
References
Full text (369.8K)
Related Articles
Aibo Liu  Department of Mathematics, Jilin University, Changchun 130012, China (email)
Changchun Liu  Department of Mathematics, and Key Laboratory of Symbolic Computation, and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China (email)
1 
S. J. Deng, W. K. Wang and H. L. Zhao, Existence theory and $L^p$ estimates for the solution of nonlinear viscous wave equation, Nonlinear Anal. Real World Appl., 11 (2010), 44044414. 

2 
L. Duan, S. Q. Liu and H. J. Zhao, A note on the optimal temporal decay estimates of solutions to the CahnHilliard equation, J. Math. Anal. Appl., 372 (2010), 666678. 

3 
P. Galenko, Phasefield model with relaxation of the diffusion flux in nonequilibrium solidification of a binary system, Phys. Lett. A, 287 (2001), 190197. 

4 
P. Galenko and D. Jou, Diffuseinterface model for rapid phase transformations in nonequilibrium systems, Phys. Rev. E, 71 (2005), 046125. 

5 
G. Gompper and M. Kraus, GinzburgLandau theory of ternary amphiphilic systems. I. Gaussian interface fluctuations, Phys. Rev. E, 47 (1993), 42894300. 

6 
G. Gomppern and M. Kraus, GinzburgLandau theory of ternary amphiphilic systems. II. Monte Carlo simulations, Phys. Rev. E, 47 (1993), 43014312. 

7 
G. Gompper and J. Goos, Fluctuating interfaces in microemulsion and sponge phases, Phys. Rev. E, 50 (1994), 13251335. 

8 
D. Jou, J. CasasVazquez and G. Lebon, Extended irreversible thermodynamics, Rep. Prog. Phys., 51 (1988), 11051179. 

9 
N. Y. Li and L. F. Mi, Pointwise estimates of solutions for the CahnHilliard equation with inertial term in multidimensions, J. Math. Anal. Appl., 397 (2013), 7587. 

10 
C. Liu and Z. Wang, Time periodic solutions for a sixth order nonlinear parabolic equation in two space dimensions, Commun. Pure Appl. Anal., 13 (2014), 10871104. 

11 
C. Liu and Z. Wang, Optimal control for a sixth order nonlinear parabolic equation, Mathematical Methods in the Applied Sciences, 38 (2015), 247262. 

12 
C. Liu, Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions, Annales Polonici Mathematici, 107 (2013), 271291. 

13 
I. Pawłow and W. Zajăczkowski, A sixth order CahnHilliard type equation arising in oilwatersurfactant mixtures, Commun. Pure Appl. Anal., 10 (2011), 18231847. 

14 
G. Schimperna and I. Pawłow, On a class of CahnHilliard models with nonlinear diffusion, SIAM J. Math. Anal., 45 (2013), 3163. 

15 
W. K. Wang and W. J. Wang, The pointwise estimates of solutions for semilinear dissipative wave equation in multidimensions, J. Math. Anal. Appl., 366 (2010), 226241. 

16 
W. K. Wang and Z. G. Wu, Optimal decay rate of solutions for CahnHilliard equation with inertial term in multidimensions, J. Math. Anal. Appl., 387 (2012), 349358. 

Go to top
