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Open Access Research

Singular degenerate problems occurring in biosorption process

Aida Sahmurova1 and Veli B Shakhmurov2*

Author Affiliations

1 Department of Environmental Sciences, Okan University, Akfirat, Tuzla, Istanbul, 34959, Turkey

2 Department of Mechanical Engineering, Okan University, Akfirat, Tuzla, Istanbul, 34959, Turkey

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Boundary Value Problems 2013, 2013:30  doi:10.1186/1687-2770-2013-30

Published: 15 February 2013

Abstract

The boundary value problems for singular degenerate arbitrary order differential-operator equations with variable coefficients are considered. The uniform coercivity properties of ordinary and partial differential equations with small parameters are derived in abstract <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/30/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/30/mathml/M1">View MathML</a> spaces. It is shown that corresponding differential operators are positive and also are generators of analytic semigroups. In application, well-posedeness of the Cauchy problem for an abstract parabolic equation and systems of parabolic equations are studied in mixed <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/30/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/30/mathml/M2">View MathML</a> spaces. These problems occur in fluid mechanics and environmental engineering.

MSC: 34G10, 35J25, 35J70.

Keywords:
differential-operator equations; degenerate equations; semigroups of operators; Banach-valued function spaces; coercive problems; operator-valued Fourier multipliers; interpolation of Banach spaces