Recurrence formula for any order evolution equations
, 2022 Riccati's differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati's differential equation with the Cole-Hopf transform shows a relation between the first order evolution equations and ...
Iwata, Yoritaka
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Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations [PDF]
, 2020 [EN] The benefits and properties of iterative splitting methods, which are based on serial versions, have been studied in recent years, this work, we extend the iterative splitting methods to novel classes of parallel versions to solve nonlinear ...
Geiser, Jürgen +2 more
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New versions of iterative splitting methods for the momentum equation [PDF]
, 2017 [EN] In this paper we propose some modifications in the schemes for the iterative splitting techniques defined in Geiser (2009) for partial differential equations and introduce the parallel version of these modified algorithms.
Eulalia Martínez +17 more
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Functional Inequalities and Subordination: Stability of Nash and Poincar\'e inequalities [PDF]
, 2011 We show that certain functional inequalities, e.g.\ Nash-type and Poincar\'e-type inequalities, for infinitesimal generators of $C_0$ semigroups are preserved under subordination in the sense of Bochner.
Schilling, René L., Wang, Jian
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On Relations Between Urbanik and Mehler Semigroups [PDF]
, 2008 It is shown that operator-selfdecomposable measures, or more precisely their Urbanik decomposability semigroups, induce generalized Mehler semigroups of bounded linear operators.
Jurek, Zbigniew J.
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Sharp extensions and algebraic properties for solution families of vector-valued differential equations [PDF]
, 2016 In this paper we show the unexpected property that extension from local to global without loss of regularity holds for the solutions of a wide class of vector-valued differential equations, in particular for the class of fractional abstract Cauchy ...
Abadias, L., Lizama, C., Miana, P.J.
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Super-Poincar\'e and Nash-type inequalities for Subordinated Semigroups [PDF]
, 2012 We prove that if a super-Poincar\'e inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincar\'e inequality for $-g(A)$ with any Bernstein function $g$. We also study the
Gentil, Ivan, Maheux, Patrick
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Abstract cauchy problems for quasi-linear evolution equations in the sense of hadamard [PDF]
, 2004 thispaper is devoted to the well-posedness of abstract cauchy problems for quasi-linear evolution equations. the notion of hadamard well-posedness is considered, and a new type of stability condition is introduced from the viewpoint of the theory of ...
Tanaka, Naoki
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On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation
, 2023 In this paper, we establish local well-posedness of the Cauchy problem for a recently proposed dispersion generalized Camassa-Holm equation by using Kato's semigroup approach for quasi-linear evolution equations.
Ayhan, Nesibe, Mutlubas, Nilay Duruk
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