Nonlinear Functional Parabolic Equations

Leo Simon

Chapter 30 in Integral Methods in Science and Engineering, Volume 2, 2010, pp 321-326 from Springer

Abstract: 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].

Date: 2010
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DOI: 10.1007/978-0-8176-4897-8_30

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