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Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions

Czernous W., Jaruszewska-Walczak D.

Opuscula Mathematica

2014

Vol. 34, no. 2

311--326

We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional differential equations. Difference methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite difference systems. Methods of second type are truncation of the infinite difference system, so that the resulting difference problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-differential problems can be obtained from the general model by specifying the given operators.

A dynamical inverse problem for a parabolic equation

Maksimov V.

Opuscula Mathematica

2006

Vol. 26, no. 2

327-342

A problem of dynamical reconstruction of unknown distributed or boundary disturbances acting upon nonlinear parabolic equations is discussed. A regularized algorithm which allows us to reconstruct disturbances synchro with the process under consideration is designed. This algorithm is stable with respect to informational noises and computational errors.

Regularity of solutions of nonlinear parabolic equations

Napiórkowska J.

Demonstratio Mathematica

2001

Vol. 34, nr 3

593-608