Initial-boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermo diffusion in solid body

Zeitschrift für Analysis und ihre Anwendungen

Volumn 19, Issue 1, 2000, Pages 121-130

  Gawinecki, J ^a   Kacprzyk, P ^a   Bar Yoseph, P ^b  

^a MILITARY UNIVERSITY OF TECHNOLOGY   (Poland)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Banach fixed point theorem; Energy estimates; Initial boundary value problems; Linear and nonlinear parabolic systems of partial differential equations; Semigroup theory; Sobolev spaces

Indexed keywords

EID: 26444452186     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. Adams, R. A.: Sobolev Spaces. New York: Academic Press 1973.
2. Aleksiewicz, A.: Functional Analysis (in Polish). Warszawa: Polish Sci. Publ. (PWN) 1969.
3. Gawinecki, J.: The Faedo-Galerkin method in thermal stresses theory. Comment. Math. 27 (1987), 83 - 101.
4. Gawinecki, J.: Global solution to initial value problems in nonlinear hyperbolic thermoelasticity (Diss. Math.: Vol. 344). Warsaw: Inst. Math. Polish Acad. Sci. 1995, pp. 1 - 61.
5. Gawinecki, J. and P. Kacprzyk: Existence, uniqueness and regularity of the solution of the first boundary-initial value problem of linear thermodiffusion in micropolar medium. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 3 (1994), 341 - 359.
6. Gawinecki, J. and K. Sierpiński: Existence, uniqueness and regularity of the solution of the first boundary-initial value problem for the equations of thermodiffusion in a solid body. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 30 (1982) 11 - 12, 163 - 171.
7. Gawinecki, J., Kacprzyk, K. and J. Jȩdrzejewski: An energy estimate for some coupled parabolic system of partial differential equations. Biul. WAT 45 (1996)12, 5 - 13.
8. Kato, T.: Abstract Differential Equations and Nonlinear Mixed Problems Centre for Pure and Appl. Math., Raport University of California, Berkeley, Published in Fermi Lecture, Scuola Normale, Pisa 1985.
9. Ladyzhenskaya, O. A., Solonnikov, V. A. and N. N. Uralceva: Linear and Quasi-Linear Equations of Parabolic Types (Trans. Math. Monographs: Vol. 23). Providence (R.I.): Amer. Math. Soc. 1968.
10. Sobolev, S. L.: Applications of Functional Analysis in Mathematical Physics (in Russian). Moskva: Nauka 1988.
11. Yosida, K.: Functional Analysis. Berlin - Heidelberg - New York: Springer Verlag 1974.
12. Zaja̧czkowski, W.: Mixed problem for nonlinear symmetric hyperbolic systems. Math. Meth. Appl. Sci. 11 (1989), 139 - 168.
13. Zaja̧czkowski, W.: Noncharacteristic mixed problems for nonlinear symmetric hyperbolic systems. Math. Meth. App. Sci. 11 (1989), 139 - 168.