# Qualitative investigation of nonlinear differential equations describing infiltration of water

Annales Polonici Mathematici (1995)

- Volume: 61, Issue: 1, page 39-57
- ISSN: 0066-2216

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topXingbao Wu. "Qualitative investigation of nonlinear differential equations describing infiltration of water." Annales Polonici Mathematici 61.1 (1995): 39-57. <http://eudml.org/doc/262308>.

@article{XingbaoWu1995,

abstract = {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.},

author = {Xingbao Wu},

journal = {Annales Polonici Mathematici},

keywords = {water percolation and seepage; similarity solution; nonlinear differential equation; qualitative behavior; water filtration problems; existence; boundedness; uniqueness},

language = {eng},

number = {1},

pages = {39-57},

title = {Qualitative investigation of nonlinear differential equations describing infiltration of water},

url = {http://eudml.org/doc/262308},

volume = {61},

year = {1995},

}

TY - JOUR

AU - Xingbao Wu

TI - Qualitative investigation of nonlinear differential equations describing infiltration of water

JO - Annales Polonici Mathematici

PY - 1995

VL - 61

IS - 1

SP - 39

EP - 57

AB - 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.

LA - eng

KW - water percolation and seepage; similarity solution; nonlinear differential equation; qualitative behavior; water filtration problems; existence; boundedness; uniqueness

UR - http://eudml.org/doc/262308

ER -

## References

top- [1] F. V. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379. Zbl0249.35043
- [2] F. V. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal. 54 (1974), 373-392. Zbl0293.35039
- [3] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, 1984.
- [4] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
- [5] R. C. Buck and E. F. Buck, Advanced Calculus, McGraw-Hill, 1978. Zbl0385.26002
- [6] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Academic Publ., 1990.
- [7] W. Okrasiński, On a nonlinear differential equation, Ann. Polon. Math. 49 (1989), 237-245. Zbl0685.34038
- [8] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, Ann. Polon. Math. 57 (1992), 71-82. Zbl0774.34017
- [9] S. Staněk, Qualitative behavior of a class of second order nonlinear differential equations on halfline, Ann. Polon. Math. 58 (1993), 65-83. Zbl0777.34027

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