On a fractional partial differential equation with dominating linear part

Mathematical Methods in the Applied Sciences

Volumn 20, Issue 16, 1997, Pages 1427-1448

  Gripenberg, G ^a   Londen, S O ^b   Pruss J ^c  

^a UNIVERSITY OF HELSINKI   (Finland)

^b AALTO UNIVERSITY   (Finland)

^c MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; INTEGRAL EQUATIONS; SET THEORY;

INITIAL CONDITIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031270541     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19971110)20:16<1427::AID-MMA937>3.0.CO;2-Y     Document Type: Article

References (10)

1. Ball, J. M., Holmes, P. J., James, R. D., Pego, R. L. and Swart, P. J., 'On the dynamics of fine structure', J. Nonlinear Science 1, 17-70 (1991).
2. Brandon, D., private communication.
3. Engler, H., 'Global smooth solutions for a class of parabolic integrodifferential equations', Trans. Amer. Math. Soc. 348, 267-290 (1996).
4. Fonseca, I., Brandon, D. and Swart, P., Dynamics and Oscillatory Microstructure in a Model of Displacive Phase Transformations, Carnegie Mellon University, Center for Nonlinear Analysis, Res. Rep. No. 94-NA-035, 1994.
5. Gripenberg, G., 'Global existence of solutions of Volterra integrodifferential equations of parabolic type', J. Differential Equations 178, 156-164 (1993).
6. Gripenberg, G., 'Weak solutions of hyperbolic-parabolic Volterra equations', Trans. Amer. Math. Soc. 343, 675-694 (1994).
7. Gripenberg, G., Londen, S.-O. and Staffans, O., Volterra Integral and Functional Equations, Cambridge University Press, Cambridge, 1990.
8. Pego, R.L. 'Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability', Arch. Ratl. Mech. Anal. 97, 353-394 (1987).
9. Prüss, J., Evolutionary Integral Equations and Applications, Birkhäuser, Basel, 1993.
10. Shea, D.F. and Wainger, S., 'Variants of the Wiener-Lévy theorem, with applications to stability problems for some Volterra integral equations', Am. J. Math. 97, 312-343 (1975).