Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakly singular kernel, we find conditions on the initial datum and on the source term of the equation to control the asymptotic behaviour of the mean temperatures.
Czasopismo
Rocznik
Tom
Strony
5--32
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Departamento de Mateḿatica Facultad de Ciencias Exactas, Ing. y Agrim. Universidad Nacional de Rosario Av. Pellegrini 250, 2000 Rosario, Argentina
autor
- Dipartimento di Matematica Pura e Applicata Universita degli Studi di Padova Via Belzoni, 7, 35131, Padova, Italy
Bibliografia
- Berrone, L.R. (1994) Mathematical letters to L. T. Villa. Rosario, January 6 and 15.
- Berrone, L.R., Tarzia, D.A.and Villa, L.T. (2000) Asymptotic behavior of a non-classical heat conduction problem for a semi-infinite material. Math. Meth. Appl. Sci.23, 1161–1177.
- Cannon, J.R. (1984) The One-Dimensional Heat Equation. Adison-Wesley, Menlo Park.
- Gawinecki, J. (1995) Global solutions to initial value problem in nonlinear hyperbolic thermoelasticity. Dissertationes Math. 344, 1–61.
- Gyori, I.and Ladas, G. (1991) Oscillation Theory of Delay Differential Equations. Clarendon Press, Oxford.
- Gripenberg, G., Londen, S.-O.and Staffans, O. (1990) Volterra Integraland Functional Equations, Encyclopedia of Mathematics and its Applications. Cambridge University Press.
- Hale, J.K.and Verduyn Lunel, S.M. (1993) Introduction to Functional Differential Equations. Springer, New York.
- Kenmochi, N.and Primicerio, M. (1988) One-Dimensional Heat Conduction with a Class of Automatic Heat-Source Controls. IMA J. Appl. Math.40, 205–216.
- Klainerman, S. (1981) Global, small amplitude solution to nonlinear evolution equations.Comm. Pure Appl. Math.34, 481–524.
- Lions, J.L. (1969) Quelques ḿethodes de resolutions de problemes aux limites non lineaires. Dunod, Gautier Villars, Paris.
- Miller, R.K. (1971) Nonlinear Volterra Integral Equations. W. A. Benjamin, Menlo Park, 1971.
- Racke R. (1992) Lectures on Nonlinear Evolution Equations. Aspect of Mathematics, E19, Vieweg.
- Saaty, L.T. (1967) Modern Nonlinear Equations. McGraw-Hill, New York.
- Tarzia, D.A. and Villa, L.T. (1990) Remarks on some nonlinear initialboundary value problems in heat conduction. Rev. U.M.A. 35, 265–275.
- Villa, L.T. (1986) Problemas de control para una ecuacíon unidimensional del calor.Rev. U.M.A.33, 163–169.
- Walter, W. (1970) Differential and Integral Inequalities. Springer, Berlin-Heidelberg, 1970.
- Wheeden, L.R.and Zygmund, A. (1977) Measure and Integral (An Introduction to Real Analysis). M. Dekker, New York.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0039