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Analyticity of nonlinear semigroups
Israel Journal of Mathematics, 1989The Cauchy problemdu/dt =Au(t),u(0) =u 0∈D(A) has analytic solutions whenA has first and second Gateaux derivatives along the solution curve in a certain weak sense. HereA is a maximal monotone operator in a complex Hilbert space.
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Elliptic Operators and Analytic Semigroups
2021In this chapter, taking advantage of the results proved in all the previous chapters, we show that the semigroups considered in Chapters 6 to 9 are analytic and we characterize the interpolations spaces of order α and 1
Luca Lorenzi, Abdelaziz Rhandi
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Analytic semigroups generated by ultraweak operators
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1991SynopsisLet Ω be a regular open subset ofRN. We present an improved generation result for nonvariational operators inL1(Ω). This result is obtained by studying ultraweak operators and by proving generation of analytic semigroups inLp(Ω)(l<p≦∞) and in. We also characterise interpolation and extrapolation spaces.
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Analyticity of the Cox–Ingersoll–Ross semigroup
Positivity, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fornaro S., Metafune G.
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Nonlinear semigroups analytic on sectors
2016This article deals with semigroups of bounded operators in a complex Banach space \(X\); these semigroups are defined and analytic on an open sector \(\Sigma= \{se^{i\phi}+ te^{i\psi}: s,t> 0\}\) in the complex plain \(\mathbb{C}\) and describe solutions of nonlinear evolution equations of type \[ {d\over d\xi} u(\xi)= Au(\xi)\quad (\xi\in \Sigma ...
Nakamura, Gen +2 more
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Maximal L1-Regularity of Generators for Bounded Analytic Semigroups in Banach Spaces
Acta Mathematica Scientia, 2022Myong‐Hwan Ri, R. Farwig
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Analytic semigroups and interpolation
2018Throughout the chapter X is a complex Banach space, A : D(A) ⊂ X ↦ X is a sectorial operator (i.e., a linear operator satisfying (5.1)), and e tA is the semigroup generated by A.
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THE WEISS CONJECTURE FOR BOUNDED ANALYTIC SEMIGROUPS
Journal of the London Mathematical Society, 2003The present paper is concerned with the so-called Weiss conjecture on admissible operators for bounded semigroups. Let \(-A\) be the generator of a \(C_0\)-semigroup \((T_t)_{t\geq 0}\) on a Banach space \(X\). A linear bounded operator \(C\) from \(D(-A)\), the domain of \(-A\), to another Banach space is called admissible for \(A\) if there is a ...
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Sesquilinear Forms and Analytic Semigroups
2014Applying the theorems of Hille–Yosida or Lumer–Phillips is sometimes unsatisfactory, as they make no claim about possible regularity gain (either in space or time) of solutions. In this chapter we specialize our previous investigations to parabolic equations.
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