Перейти до основного вмісту
Mixed problems for anisotropic second-order elliptic-parabolic equations in unbounded domains
Bokalo Mykola Mykhailovych 1
1 Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, Lviv, 79007, Ukraine
Keywords: mixed problems, anisotropic second-order elliptic-parabolic equations
Abstract
The present paper is devoted to elliptic-parabolic anisotropic second order equations in unbounded domains. We establish conditions for the existence and uniqueness of generalized solutions of initial-boundary value problems and estimate the solutions without any restrictions on the growth of the data-in and the behavior of the solutions at infinity.
References

[1] Brézis H. Semilinear equations in $\mathbb{R}^N$ without condition at infinity // Appl. Math. Optim. – 1984. – 12 , N3. – P. 271-282.

[2] Bernis F. Elliptic and parabolic semilinear problems without conditions at infinity // Arch. Rational Mech. Anal. – 1989. – 106, N3. – P. 217-241.

[3] Gladkov A., Guedda M. Diffusion-absorption equation without growth restridtions on the data at infinity // J. Math. Anal. Appl. – 2002. – 269 , N1. – P. 16-37.

[4] Bokalo M.M., Pauchok I.B. On the correctness of the Fourier problem for nonlinear parabolic equations of higher orders with variable nonlinearity indices // Mat. studii. – 2006. – 24, N1. – P. 25-48.

[5] Bokalo M., Domanska O. On well-posedness of boundary problems for elliptic equations in general anisotropic Lebesgue-Sobolev spaces // Math. studii. – 2007. – 28 , N1. – P. 77-91.

[6] Medved I. Problems for nonlinear elliptic and parabolic equations in anisotropic spaces // Lviv Univ. Bulletin. Series of Mech.-Mat. - 2005. - 64. - P. 149-166.

[7] Bugriy O.M. Problem with initial condition for nonlinear parabolic variational inequality in the unbounded domain by spatial variables // Lviv Univ. Ser. meh.-mat. - 2007. - 67. - P. 30-52.

[8] Kuttler K.L., Jr. The Galerkin method and degenerate evolution equations // Journal of Mathematical Analysis and Applications. – 1985. – 107 . – P. 396-413.

[9] Showalter R.E. Monotone operators in Banach space and nonlinear partial differential equations. – Mathematical surveys and monographs, 49. – Amer. Math. Soc., Providence, 1997.

[10] Lyons J.-L. Some methods for solving nonlinear boundary value problems. - M., 1972.

Cite
ACS Style
Bokalo, M.M. Mixed problems for anisotropic second-order elliptic-parabolic equations in unbounded domains. Bukovinian Mathematical Journal. 2016, 1
AMA Style
Bokalo MM. Mixed problems for anisotropic second-order elliptic-parabolic equations in unbounded domains. Bukovinian Mathematical Journal. 2016; 1(3-4).
Chicago/Turabian Style
Mykola Mykhailovych Bokalo. 2016. "Mixed problems for anisotropic second-order elliptic-parabolic equations in unbounded domains". Bukovinian Mathematical Journal. 1 no. 3-4.
Export
We use own, third-party cookies, and localStorage files to analyze web traffic and page activities. Privacy Policy Settings