Analytic Semigroups and Optimal Regularity in Parabolic Problems

By A. Lunardi. 2003

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Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4e6617a8248b6a2c91ebf2c039cae2fe556c514d

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In Computational Theory and Mathematics

Citations in the corpus

Quasilinear parabolic problems via maximal regularity (2005, methodology): “We also refer to Clément and Simonett [10] for a study of (0.1) using maximal regularity in continuous interpolation spaces, extending and improving on earlier results of Da Prato and Grisvard [11] and Angenent [7], as well as to the book by Lunardi [14] who bases her studies on maximal regularity ”
Elliptic and parabolic equations for measures (2009, result): “Certainly, once the existence of densities is established, in many cases one can apply the results known for functions (but taking special care of the form of the equation), in particular, the results from [108], [111], [116], [123].”
Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional–differential equations and applications (2007, background): “Note that the assumption (H2) is achieved in many cases, see, for instance, Lunardi [20], and the section devoted to applications in Rankin [26].”
Dissipative Gradient Nonlinearities Prevent δ$\delta$ ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models (2024, positive): “As a consequence, by recalling that [33, Theorem 7.3.3] ensures the existence of some 0 T 1 , as above, such that problem (21) has a unique solution In particular, this produces some positive constant K = K (˜ u, ∇ v, ∇ w, u 0 ) , and henceforth K = K ( R ) , with the property that | u ( x, t )…”
On quasilinear parabolic evolution equations in weighted Lp-spaces (2009, background): “r BUCµ([0,T];X) := {u ∈ C((0,T];X) : t1−µu ∈ BUC((0,T];X), lim t→0+ t1−µ|u(t)| X = 0}, µ ∈ (0,1]. as a basic space, instead of (1.2). Concerning the long-time behaviour of solutions, we refer e.g. to [7, 17, 18, 19, 22, 24]. It is one aim of this paper to extend the local convergenceresult [22, Theo”
Sharp embedding results for spaces of smooth functions with power weights (2011, background): “For evolution equations, power weights in time play an important role in order to obtain results for rough initial data (see [11, 20, 25, 31]).”