Abstract:
The behavior of solutions of a parabolic problem of gas or fluid flow in porous media was studied. The existence of globally bounded weak solutions or blow-up for the problem was analyzed. Adequate supersolutions and subsolutions were constructed and the results about global existence of weak solutions were proved.
Registro:
Documento: |
Artículo
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Título: | Porous medium equation with absorption and a nonlinear boundary condition |
Autor: | Andreu, F.; Mazón, J.M.; Toledo, J.; Rossi, J.D. |
Filiación: | Departament De Matemàtiques, Universitat De València, Valencia, Spain Departamento De Matemática, F.C.E y N., UBA, 1428 Buenos Aires, Argentina
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Palabras clave: | Blow up; Global existence; Nonlinear boundary conditions; Porous medium equation; Absorption; Boundary conditions; Mathematical models; Porous materials; Nonlinear boundary conditions; Nonlinear equations |
Año: | 2002
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Volumen: | 49
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Número: | 4
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Página de inicio: | 541
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Página de fin: | 563
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DOI: |
http://dx.doi.org/10.1016/S0362-546X(01)00122-5 |
Título revista: | Nonlinear Analysis, Theory, Methods and Applications
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Título revista abreviado: | Nonlinear Anal Theory Methods Appl
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ISSN: | 0362546X
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CODEN: | NOAND
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v49_n4_p541_Andreu |
Referencias:
- Anderson, J.R., Local existence and uniqueness of solutions of degenerate parabolic equations (1991) Comm. Partial Differential Equations, 16, pp. 105-143
- Andreu, F., Mazón, J.M., Simondon, F., Toledo, J., Attractor for a degenerate nonlinear diffusion problem with nonlinear boundary condition (1998) J. Dynamic Differential Equations, 10, pp. 347-377
- Aronson, D.G., The porous medium equation (1986) Nonlinear Diffusion Problems, 1224. , Fasano, Primicerio (Eds.), Springer, Berlin, L.N.M
- Bénilan, Ph., Cortázar, C., Elgueta, M., Uniqueness and non-uniqueness of the solutions of a mixed boundary value problem for the porous medium equation (1991) Rev. Un. Mat. Argentina, 37, pp. 10-15
- Chipot, M., Fila, M., Quittner, P., Stationary solutions, blow-up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions (1991) Acta Math. Univ. Comenianae, 60, pp. 35-103
- Cortazar, C., Elgueta, M., Rossi, J.D., Uniqueness and non-uniqueness for the porous medium equation with nonlinear boundary conditions, , Preprint
- DiBenedetto, E., Continuity of weak solutions to a general porous medium equation (1983) Indiana Univ. Math. J., 32, pp. 83-118
- Filo, J., De Mottoni, P., Global existence and decay of solutions of the porous medium equation with nonlinear boundary conditions (1992) Commun. Partial Differential Equations, 17, pp. 737-765
- Galaktionov, V.A., Levine, H.A., On critical Fujita exponents for heat equations with nonlinear flux boundary conditions on the boundary (1996) Israel J. Math., 94, pp. 125-146
- Gilding, B.H., On a class of similarity solutions of the porous media equation III (1980) J. Math. Anal. Appl., 77, pp. 381-402
- Gilding, B.H., Peletier, L.A., On a class of similarity solutions of the porous media equation (1976) J. Math. Anal. Appl., 55, pp. 351-364
- Gilding, B.H., Peletier, L.A., On a class of similarity solutions of the porous media equation II (1977) J. Math. Anal. Appl., 57, pp. 522-538
- Gurtin, M.E., Mac Cammy, R.C., On the diffusion of biological population (1977) Math. Biosci., 33, pp. 35-49
- Ladyzenskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N., Linear and Quasilinear Equations of Parabolic Type (1968) AMS Translational Monograph, 23. , Providence, RI
- Morrey Jr., C.B., (1966) Multiple Integrals in the Calculus of Variations, , Springer, Berlin
- Quittner, P., On global existence and stationary solutions for two classes of semilinear parabolic problems (1993) Comment. Math. Univ. Caroline, 34, pp. 105-124
- Temam, R., (1988) Infinite-Dimensional Dynamical Systems in Mechanics and Physics, , Springer, Berlin
- Walter, W., On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition (1975) SIAM J. Math. Anal., 6 (1), pp. 85-90
Citas:
---------- APA ----------
Andreu, F., Mazón, J.M., Toledo, J. & Rossi, J.D.
(2002)
. Porous medium equation with absorption and a nonlinear boundary condition. Nonlinear Analysis, Theory, Methods and Applications, 49(4), 541-563.
http://dx.doi.org/10.1016/S0362-546X(01)00122-5---------- CHICAGO ----------
Andreu, F., Mazón, J.M., Toledo, J., Rossi, J.D.
"Porous medium equation with absorption and a nonlinear boundary condition"
. Nonlinear Analysis, Theory, Methods and Applications 49, no. 4
(2002) : 541-563.
http://dx.doi.org/10.1016/S0362-546X(01)00122-5---------- MLA ----------
Andreu, F., Mazón, J.M., Toledo, J., Rossi, J.D.
"Porous medium equation with absorption and a nonlinear boundary condition"
. Nonlinear Analysis, Theory, Methods and Applications, vol. 49, no. 4, 2002, pp. 541-563.
http://dx.doi.org/10.1016/S0362-546X(01)00122-5---------- VANCOUVER ----------
Andreu, F., Mazón, J.M., Toledo, J., Rossi, J.D. Porous medium equation with absorption and a nonlinear boundary condition. Nonlinear Anal Theory Methods Appl. 2002;49(4):541-563.
http://dx.doi.org/10.1016/S0362-546X(01)00122-5