caa a22 4500 605523800 CHVBK 20210128100751.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10958-015-2576-1 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2576-1 Stability of Solutions to Generalized Forchheimer Equations of any Degree [Elektronische Daten] [L. Hoang, A. Ibragimov, T. Kieu, Z. Sobol] The dynamics of generalized Forchheimer equations for slightly compressible fluids are tudied by means of initial boundary value problem for the pressure. We prove that the solutions continuously depend on the boundary data and the Forchheimer polynomials. New bounds for the solutions are established in the Lα-norm for all α ≥ 1, and then are used to improve estimates for their spatial and time derivatives. New Poincaré-Sobolev inequalities and nonlinear Gronwall type estimates for nonlinear differential inequalities are utilized to achieve better asymptotic bounds. The methods developed can be applied to other degenerate parabolic equations. Bibliography: 25 titles. Springer Science+Business Media New York, 2015 Hoang L. Texas Tech University, Box 41042 Lubbock, 79409-1042, Lubbock, TX, USA aut Ibragimov A. Texas Tech University, Box 41042 Lubbock, 79409-1042, Lubbock, TX, USA aut Kieu T. University of North Georgia, 3820 Mundy Mill RD., Oakwood, 30566, Oakwood, GA, USA aut Sobol Z. Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/4(2015-10-01), 476-544 1072-3374 210:4<476 2015 210 10958 https://doi.org/10.1007/s10958-015-2576-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2576-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hoang L. Texas Tech University, Box 41042 Lubbock, 79409-1042, Lubbock, TX, USA aut NATIONALLICENCE 700 1- Ibragimov A. Texas Tech University, Box 41042 Lubbock, 79409-1042, Lubbock, TX, USA aut NATIONALLICENCE 700 1- Kieu T. University of North Georgia, 3820 Mundy Mill RD., Oakwood, 30566, Oakwood, GA, USA aut NATIONALLICENCE 700 1- Sobol Z. Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/4(2015-10-01), 476-544 1072-3374 210:4<476 2015 210 10958