Qualitative investigation of nonlinear differential equations describing infiltration of water
Xingbao Wu
Annales Polonici Mathematici, Tome 62 (1995), p. 39-57 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262308 
@article{bwmeta1.element.bwnjournal-article-apmv61z1p39bwm,
     author = {Xingbao Wu},
     title = {Qualitative investigation of nonlinear differential equations describing infiltration of water},
     journal = {Annales Polonici Mathematici},
     volume = {62},
     year = {1995},
     pages = {39-57},
     zbl = {0827.34012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p39bwm}
}

Xingbao Wu. Qualitative investigation of nonlinear differential equations describing infiltration of water. Annales Polonici Mathematici, Tome 62 (1995) pp. 39-57. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p39bwm/

[000] [1] F. V. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379. | Zbl 0249.35043

[001] [2] F. V. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal. 54 (1974), 373-392. | Zbl 0293.35039

[002] [3] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, 1984.

[003] [4] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.

[004] [5] R. C. Buck and E. F. Buck, Advanced Calculus, McGraw-Hill, 1978. | Zbl 0385.26002

[005] [6] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Academic Publ., 1990.

[006] [7] W. Okrasiński, On a nonlinear differential equation, Ann. Polon. Math. 49 (1989), 237-245. | Zbl 0685.34038

[007] [8] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, Ann. Polon. Math. 57 (1992), 71-82. | Zbl 0774.34017

[008] [9] S. Staněk, Qualitative behavior of a class of second order nonlinear differential equations on halfline, Ann. Polon. Math. 58 (1993), 65-83. | Zbl 0777.34027