Mixed problems for a nonlinear coupled evolution system in unbounded domains

M.O.Nechepurenko

A nonlinear coupled evolution system in an unbounded domain of $R^n$ is considered. The sufficient conditions of existence and uniqueness of a solution were obtained without any restriction at infinity.

1. Apolaya R.F., Clark H.R., Feitosa A.J. On a nonlinear coupled system with internal damping // Electronic Journal of Differential Equations, Vol.2000, No. 64, pp. 1-17.

2. Clark H. R., San Gil Jutuca L. P. $\&$ Milla Miranda On a mixed problem for a linear coupled system with variable coefficients // Electronic Journal of Differential Equations. - 1998. - Vol.1. -N 04. - P.1-20.

3. Clark M.R. $\&$ Lima O.A. On a mixed problem for a coupled nonlinear system // Electronic Journal of Differential Equations.- 1997. - Vol.1997. - N. 06. - P. 1–11.

4. Lions, J. L., Magenes, E. Non-homogeneous boundary value problems and applications, V.I. - New York: Springer-Verlag, 1972.

5. Salim A. Messaoudi. A blowup result in a multidimensional semilinear thermoelastic system // Electronic Journal of Differential Equations.- 2001. - Vol. 2001. - N. 30. - P. 1-9.

6. Гаевский Х., Грегер К., Захариас К. Нелинейные операторные уравнения и операторные дифференциальные уравнения. -М., 1978.

7. Nechepurenko M.O. The mixed problem for a nonlinear coupled evolution system in a bounded domain, in print.

8. Medeiros L. A., Milla Miranda M. On a boundary value problem for wave equations: existence, uniqueness-asymptotic behavior // Revista de Matematicas Aplicadas, Universidade de Chile. - 1996. - N. 17, P. 47-73.

9. Komornik V., Zuazua E. A direct method for boundary stabilization of the wave equation // J. Math. Pure et Appl. - 1990. - № 69. - P.33-54.

10. Schiff L. I. Non-linear meson theory of nuclear forces // J. Physic. Rev. - 1951. - № 84. - P.1-9.

11. Segal I. E. The global Cauchy problem for a relativistic scalar field with power interaction // Bull. Soc. Math. France. - 1963. - № 91. - P.129-135.

12. Showalter R. E. Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. - Math. surveys and monographs. - 1996. - V.49.

	Mixed problems for a nonlinear coupled evolution system in unbounded domains
Author	M.O.Nechepurenko m.nechepurenko@allianz.ua Lviv Ivan Franko National University,Universytets'ka Str., 1, 79000,Lviv, Ukraine
Abstract	A nonlinear coupled evolution system in an unbounded domain of $R^n$ is considered. The sufficient conditions of existence and uniqueness of a solution were obtained without any restriction at infinity.
Keywords	mixed problem, nonlinear coupled evolution problem, unbounded domain
DOI	doi:10.30970/ms.32.1.33-44
Reference	1. Apolaya R.F., Clark H.R., Feitosa A.J. On a nonlinear coupled system with internal damping // Electronic Journal of Differential Equations, Vol.2000, No. 64, pp. 1-17. 2. Clark H. R., San Gil Jutuca L. P. $\&$ Milla Miranda On a mixed problem for a linear coupled system with variable coefficients // Electronic Journal of Differential Equations. - 1998. - Vol.1. -N 04. - P.1-20. 3. Clark M.R. $\&$ Lima O.A. On a mixed problem for a coupled nonlinear system // Electronic Journal of Differential Equations.- 1997. - Vol.1997. - N. 06. - P. 1–11. 4. Lions, J. L., Magenes, E. Non-homogeneous boundary value problems and applications, V.I. - New York: Springer-Verlag, 1972. 5. Salim A. Messaoudi. A blowup result in a multidimensional semilinear thermoelastic system // Electronic Journal of Differential Equations.- 2001. - Vol. 2001. - N. 30. - P. 1-9. 6. Гаевский Х., Грегер К., Захариас К. Нелинейные операторные уравнения и операторные дифференциальные уравнения. -М., 1978. 7. Nechepurenko M.O. The mixed problem for a nonlinear coupled evolution system in a bounded domain, in print. 8. Medeiros L. A., Milla Miranda M. On a boundary value problem for wave equations: existence, uniqueness-asymptotic behavior // Revista de Matematicas Aplicadas, Universidade de Chile. - 1996. - N. 17, P. 47-73. 9. Komornik V., Zuazua E. A direct method for boundary stabilization of the wave equation // J. Math. Pure et Appl. - 1990. - № 69. - P.33-54. 10. Schiff L. I. Non-linear meson theory of nuclear forces // J. Physic. Rev. - 1951. - № 84. - P.1-9. 11. Segal I. E. The global Cauchy problem for a relativistic scalar field with power interaction // Bull. Soc. Math. France. - 1963. - № 91. - P.129-135. 12. Showalter R. E. Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. - Math. surveys and monographs. - 1996. - V.49.
Pages	33-44
Volume	32
Issue	1
Year	2009
Journal	Matematychni Studii
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