In this paper, we present some results regarding existence and uniqueness of solution on Lp-spaces, 1 < p < + ∞, to a nonlinear initial boundary value problem originally proposed by Lebowitz and Rubinow (J Math Biol 1:17–36, 1974) to model an age-structured cell population with inherited properties. Our results complete those obtained by Garcia-Falset (Math Meth Appl Sci 34:1658–1666, 2011).
Mathematics Subject Classification
Primary 147H06 Secondary 34A12 35F20
Evolution equation local boundary conditions quasi-accretive operators mild and strong solutions
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Boulanouar M.: A model of proliferating cell populations with infinite cell cycle length: asymptotic behavior. Acta Appl. Math. 110, 1105–1126 (2010)MathSciNetCrossRefMATHGoogle Scholar
Browder F.E.: Nonlinear mappings of nonexpansive and accretive type in Banach spaces. Bull. Am. Math. Soc. 7(3), 875–882 (1968)MathSciNetMATHGoogle Scholar
Garcia-Falset J.: Well-posedness of a nonlinear evolution equation arising in growing cell population. Math. Methods Appl. Sci. 34, 1658–1666 (2011)MathSciNetCrossRefMATHGoogle Scholar
Garcia-Falset J., Latrach K., Zeghal A.: Existence and uniqueness results for a nonlinear evolution equation arising in growing cell populations. Nonlinear Anal. 97, 210–227 (2014)MathSciNetCrossRefMATHGoogle Scholar
Latrach K., Mokhtar-Kharroubi M.: On an unbounded linear operator arising in the theory of growing cell population. J. Math. Anal. Appl. 211, 273–294 (1997)MathSciNetCrossRefMATHGoogle Scholar
Latrach K., Taoudi M.A., Zeghal A.: On the solvability of a nonlinear boundary value problem arising in the theory of growing cell populations. Math. Methods Appl. Sci. 28(8), 991–1006 (2005)MathSciNetCrossRefMATHGoogle Scholar
Shanthidevi C.N., Matsumoto T., Oharu S.: Nonlinear semigroup approach to age structured proliferating cell population with inherited cycle length. Nonlinear Anal. Real World Appl. 9, 1905–1917 (2008)MathSciNetCrossRefMATHGoogle Scholar