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Nonlinear Functional Parabolic Equations

In: Integral Methods in Science and Engineering, Volume 2

Author

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  • L. Simon

    (L. Eötvös University of Budapest)

Abstract

This work was motivated by works where nonlinear parabolic functional differential equations were considered which arise in certain applications. (See the references in [SiJa08].) In [SiJa08], existence theorems and some qualitative properties were proved on solutions to initial value problems for the functional equations (connected with the above applications) 30.1 $$D_t u - \sum_{i=1}^n D_i[a_i(t, x, u, Du; u)] + a_0(t, x, u, Du; u) = f.$$ The aim of this chapter is to formulate existence theorems if certain modified (in some sense more general) assumptions are fulfilled and to show several examples satisfying these conditions such that the assumptions of [SiJa08] are not fulfilled. Some qualitative properties of the solutions are proved in [Si09].

Suggested Citation

  • L. Simon, 2010. "Nonlinear Functional Parabolic Equations," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 2, chapter 30, pages 321-326, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4897-8_30
    DOI: 10.1007/978-0-8176-4897-8_30
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