Parabolic problem for filtration-absorption equation without conditions at infinity (in Ukrainian)

I.M.Medvid

We prove existence of a solution of some nonlinear parabolic problem without conditions at infinity. In particular, the growth of the data and coefficients of equation at infinity need not be bounded.

1. Brezis H. Semilinear equations in $\mathbb{R}^{n}$ without conditions at infinity, Appl. Math. Optim,. 1984, Vol. 12. no 3, P. 271--282.

2. Pierre M. Nonlinear fast diffusion with measures as data. In ``Nonlinear parabolic equations: qualitative properties of solutions'' , ed. by L. Boccardo and A. Tesei. Pitman Research Notes in Mathematics, 1987, 149, P. 179--188.

3. Bernis Francisco Elliptic and parabolic semilinear problems without conditions at infinity, Arch. Rational Mech. Anal, 1989, Vol. 106, no 3, P.217--241.

4. Di Benedetto, Herrero M.A. Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when $1
5. McLeod B., Pelitier L.A., Vazquez J.L. Solutions of nonlinear Ode appearing in the theory of diffusion with absorption, Differential Integral Equations, 1991, Vol. 4, no 1, P.1--14.

6. Vazquez J.L., Walias M. Existence and uniqueness of solutions of diffusion-absorption equations with general data, Differential Integral Equations, 1994, Vol. 7, no 1, P.15--36.

7. Бокало Н.М. Краевые задачи для полулинейных параболических уравнений в неограниченных областях без условий на бесконечности, Сиб. мат. журн., 1996, Т. 37, № 5, С. 977--985.

8. Gladkov A., Guedda M. Diffusion-absorption equation without growth restrictions on the data at infinity, J. Math. Anal. Appl, 2002, Vol. 274, no 1, P. 16--37.

9. Marchi C, Tesei A. Higher-order parabolic equations without conditions at infinity, J. Math. Anal. Appl, 2002, Vol. 269, no 1, P. 352--368.

10. Herrero M.A., Vel\'azquez J.J.L. On the dynamics of a semilinear heat equation with strong absorption, Comm. Part. Differ. Equat., 1989, V. 14, no 12, P. 1653--1715.

11. Бокало М., Дмитрів В. Крайові задачі для інтегро-диференціальних рівнянь в анізотропних просторах // Вісник Львів. ун-ту. Серія мех.-мат., 2001, Вип.59. С.84--101.

12. Bokalo M.M., Sikorsky V.M. The well-posedness of a Fourier problem for quasilinear parabolic equations of arbitrary order in unisotropic spaces, Mat. Studii, 1997, Vol. 8, no 1, P. 53--70.

13. Лионс Ж.-Л. Некоторые методы решения нелинейных краевых задач. -- Москва: Мир, 1972. -- 608~с.

14. Коддингтон Э.А., Левинсон Н. Теория обыкновенных дифференциальных уравнений. -- Москва: Изд-во иностранной литературы, 1958. -- 475~с.

15. Гаевский Х., Грегер К., Захариас К. Нелинейные операторные уравнения и операторные дифференциальные уравнения. -- Москва: Мир, 1978. -- 336~с.

	Parabolic problem for filtration-absorption equation without conditions at infinity (in Ukrainian)
Author	I.M.Medvid Ivan Franko National University of Lviv
Abstract	We prove existence of a solution of some nonlinear parabolic problem without conditions at infinity. In particular, the growth of the data and coefficients of equation at infinity need not be bounded.
Keywords	parabolic problem, filtration-absorption equation, existence of solution
DOI	doi:10.30970/ms.26.2.202-211
Reference	1. Brezis H. Semilinear equations in $\mathbb{R}^{n}$ without conditions at infinity, Appl. Math. Optim,. 1984, Vol. 12. no 3, P. 271--282. 2. Pierre M. Nonlinear fast diffusion with measures as data. In ``Nonlinear parabolic equations: qualitative properties of solutions'' , ed. by L. Boccardo and A. Tesei. Pitman Research Notes in Mathematics, 1987, 149, P. 179--188. 3. Bernis Francisco Elliptic and parabolic semilinear problems without conditions at infinity, Arch. Rational Mech. Anal, 1989, Vol. 106, no 3, P.217--241. 4. Di Benedetto, Herrero M.A. Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when $1 5. McLeod B., Pelitier L.A., Vazquez J.L. Solutions of nonlinear Ode appearing in the theory of diffusion with absorption, Differential Integral Equations, 1991, Vol. 4, no 1, P.1--14. 6. Vazquez J.L., Walias M. Existence and uniqueness of solutions of diffusion-absorption equations with general data, Differential Integral Equations, 1994, Vol. 7, no 1, P.15--36. 7. Бокало Н.М. Краевые задачи для полулинейных параболических уравнений в неограниченных областях без условий на бесконечности, Сиб. мат. журн., 1996, Т. 37, № 5, С. 977--985. 8. Gladkov A., Guedda M. Diffusion-absorption equation without growth restrictions on the data at infinity, J. Math. Anal. Appl, 2002, Vol. 274, no 1, P. 16--37. 9. Marchi C, Tesei A. Higher-order parabolic equations without conditions at infinity, J. Math. Anal. Appl, 2002, Vol. 269, no 1, P. 352--368. 10. Herrero M.A., Vel\'azquez J.J.L. On the dynamics of a semilinear heat equation with strong absorption, Comm. Part. Differ. Equat., 1989, V. 14, no 12, P. 1653--1715. 11. Бокало М., Дмитрів В. Крайові задачі для інтегро-диференціальних рівнянь в анізотропних просторах // Вісник Львів. ун-ту. Серія мех.-мат., 2001, Вип.59. С.84--101. 12. Bokalo M.M., Sikorsky V.M. The well-posedness of a Fourier problem for quasilinear parabolic equations of arbitrary order in unisotropic spaces, Mat. Studii, 1997, Vol. 8, no 1, P. 53--70. 13. Лионс Ж.-Л. Некоторые методы решения нелинейных краевых задач. -- Москва: Мир, 1972. -- 608~с. 14. Коддингтон Э.А., Левинсон Н. Теория обыкновенных дифференциальных уравнений. -- Москва: Изд-во иностранной литературы, 1958. -- 475~с. 15. Гаевский Х., Грегер К., Захариас К. Нелинейные операторные уравнения и операторные дифференциальные уравнения. -- Москва: Мир, 1978. -- 336~с.
Pages	202-211
Volume	26
Issue	2
Year	2006
Journal	Matematychni Studii
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