Maximal Monotone Operators On Hilbert Spaces And Applications

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ABSTRACT

Let H be a real Hilbert space and A : D(A) ⊂ H → H be an unbounded, linear, self-adjoint, and maximal monotone operator. The aim of this thesis is to solve u 0 (t) + Au(t) = 0, when A is linear but not bounded. The classical theory of differential linear systems cannot be applied here because the exponential formula exp(tA) does not make sense, since A is not continuous. Here we assume A is maximal monotone on a real Hilbert space, then we use the Yosida approximation to solve. Also, we provide many results on regularity of solutions. To illustrate the basic theory of the thesis, we propose to solve the heat equation in L 2 (Ω). In order to do that, we use many important properties from Sobolev spaces, Green’s formula and Lax-Milgram’s theorem.

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APA

TUADOR, N (2021). Maximal Monotone Operators On Hilbert Spaces And Applications. Afribary. Retrieved from https://afribary.com/works/maximal-monotone-operators-on-hilbert-spaces-and-applications

MLA 8th

TUADOR, NWIGBO "Maximal Monotone Operators On Hilbert Spaces And Applications" Afribary. Afribary, 15 Apr. 2021, https://afribary.com/works/maximal-monotone-operators-on-hilbert-spaces-and-applications. Accessed 29 Mar. 2024.

MLA7

TUADOR, NWIGBO . "Maximal Monotone Operators On Hilbert Spaces And Applications". Afribary, Afribary, 15 Apr. 2021. Web. 29 Mar. 2024. < https://afribary.com/works/maximal-monotone-operators-on-hilbert-spaces-and-applications >.

Chicago

TUADOR, NWIGBO . "Maximal Monotone Operators On Hilbert Spaces And Applications" Afribary (2021). Accessed March 29, 2024. https://afribary.com/works/maximal-monotone-operators-on-hilbert-spaces-and-applications