Continuous dependence on modelling and non-existence results for a Ginzburg-Landau equation

Mathematical Methods in the Applied Sciences

Volumn 23, Issue 17, 2000, Pages 1537-1550

  Ames, Karen A ^a  

^a University of Alabama in Huntsville ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; PHASE TRANSITIONS; PROBLEM SOLVING;

GINZBURG-LANDAU EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0034320857     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1476(20001125)23:17<1537::AID-MMA159>3.0.CO;2-V     Document Type: Article

References (20)

1. Ames KA, Payne LE. On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Math. Models Methods Appl. Sci. 1994; 4: 733-740.
2. Ames KA, Payne LE. Continuous dependence results for a problem in penetrative convection. Quart. Appl. Math. 1997; 55: 769-790.
3. Ames KA, Straughan B. Non-Standard and Improperly Posed Problems, Vol 194. Mathematics in Science and Engineering Series, Academic Press: New York, 1997.
4. Bellomo N, Preziosi L. Modelling Mathematical Methods and Scientific Computation. CRC Press: Boca Raton, 1995.
5. Bennett AD. Continuous dependence on modeling in the Cauchy problem for second order nonlinear partial differential equations. Ph.D. Thesis, Cornell University, 1986.
6. Bennett AD. Continuous dependence on modeling in the Cauchy problem for elliptic equations. Differential Integral Equations 1991; 4: 1311-1324.
7. Flavin JN, Rionero S. Qualitative Estimates for Partial Differential Equations. CRC Press: Boca Raton, 1995.
8. Franchi F, Straughan B. Spatial decay estimates and continuous dependence on modelling for an equation from dynamo theory. Proc. Roy. Soc. London A 1994; 445: 437-451.
9. Franchi F, Straughan B. Structural stability for the Brinkman equations of porous media. Math. Methods. Appl. Sci. 1996; 19: 1335-1347.
10. Gao H, Duan J. On the initial-value problem for the generalized Ginzburgh-Landau equation. J. Math. Anal. Appl. 1997; 216: 536-548.
11. Katou K. Asymptotic spatial patterns on the complex time-dependent Ginzburg-Landau equation. J. Phys. A 1986; 19: 1063-1066.
12. Levine HA. Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: the method of unbounded Fourier coefficients. Math. Ann. 1975; 214: 73-81.
13. Levine HA. The role of critical exponents in blowup theorems. SIAM Rev. 1990; 32: 262-288.
14. Maugin GA, Muschik W. Thermodynamics with internal variables Part I, General Concepts. J. Non-Equib. Thermodyn. 1994; 19: 217-249.
15. Payne LE. Improperly posed problems in partial differential equations, CBMS Regional Conf. Ser. Appl. Math. SIAM: Philadelphia, PA, 1975.
16. Payne LE. On geometric and modeling perturbations in partial differential equations. In Proc. LMS Symp. on Non-Classical Continuum Mechanics, Knops RJ, Lacey AA (eds). Cambridge University Press: Cambridge, 1987; 108-128.
17. Payne LE. On stabilizing ill-posed problems against errors in geometry and modelling. In Proc. Conf. on Inverse and Ill-posed Problems: Strobhl, Engel H, Groetsch CW (eds), New York, Academic Press: New York, 1987; 399-416.
18. Payne LE, Straughan B. Error estimates for the temperature of a piece of cold ice, given data on only part of the boundary. Nonlinear Anal Theory Meth. Applic. 1990; 14: 443-452.
19. Payne LE, Weinberger HF. New bounds for solutions of second order elliptic partial differential equations. Pacific J. Math. 1958; 8: 551-573.
20. Straughan B. Instability, Nonexistence and Weighted Energy Methods in Fluid Dynamics and Related Theories. Pitman Res. Notes Math., vol. 74, Pitman: London, 1982.