Opuscula Math. 30, no. 1 (2010), 95-115

Opuscula Mathematica

Differential difference inequalities related to parabolic functional differential equations

Milena Netka

Abstract. Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.

Keywords: parabolic functional differential equations, method of lines, stability and convergence.

Mathematics Subject Classification: 35R10, 35K20, 65N40.

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  • Milena Netka
  • University of Gdańsk, Institute of Mathematics, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Received: 2009-09-16.
  • Revised: 2009-10-22.
  • Accepted: 2009-10-30.
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Cite this article as:
Milena Netka, Differential difference inequalities related to parabolic functional differential equations, Opuscula Math. 30, no. 1 (2010), 95-115, http://dx.doi.org/10.7494/OpMath.2010.30.1.95

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