On Maximal Regularity for Abstract Parabolic Problems with Fractional Time Derivative
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DOI: 10.1007/s00009-019-1309-y
Abstract: We consider initial value problems for abstract evolution equations with fractional time derivative. Concerning the Caputo derivative $$\mathbb {D}^\alpha u$$Dαu, we show that certain assumptions, which are known to be sufficient to get a unique… read more here.
Keywords: time derivative; regularity abstract; regularity; maximal regularity ... See more keywords
Maximal Regularity for Non-autonomous Evolutionary Equations
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DOI: 10.1007/s00020-021-02645-5
Abstract: We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider time-dependent partial differential equations in… read more here.
Keywords: regularity non; non autonomous; autonomous evolutionary; maximal regularity ... See more keywords
Discrete maximal regularity and the finite element method for parabolic equations
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DOI: 10.1007/s00211-017-0929-z
Abstract: Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for parabolic equations on a polygonal or polyhedral domain $$\varOmega… read more here.
Keywords: finite element; maximal regularity; parabolic equations; method ... See more keywords
On the maximal L-L regularity of solutions to a general linear parabolic system
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DOI: 10.1016/j.jde.2019.09.058
Abstract: We show the existence of solution in the maximal $L_p-L_q$ regularity framework to a class of symmetric parabolic problems on a uniformly $C^2$ domain in ${\mathcal R}$. Our approach consist in showing ${\mathcal R}$ -… read more here.
Keywords: maximal regularity; linear parabolic; regularity; general linear ... See more keywords
Kinetic maximal L-regularity with temporal weights and application to quasilinear kinetic diffusion equations
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DOI: 10.1016/j.jde.2021.10.043
Abstract: We introduce the concept of kinetic maximal $L^p$-regularity with temporal weights and prove that this property is satisfied for the (fractional) Kolmogorov equation. We show that solutions are continuous with values in the trace space… read more here.
Keywords: quasilinear kinetic; temporal weights; regularity temporal; kinetic maximal ... See more keywords
Maximal ℓp-regularity for discrete time Volterra equations with delay
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2019.1638916
Abstract: ABSTRACT In this paper, we investigate the existence and uniqueness of solutions belonging to the vector-valued space by using Blunck's theorem on the equivalence between operator-valued -multipliers and the notion of R-boundedness for the discrete… read more here.
Keywords: discrete time; time; time volterra; regularity discrete ... See more keywords