Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients

By Rico Zacher. 2008

101 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/f6dd87c441cb9dfdcf551502f04015628b2644fe

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Citations in the corpus

Time fractional diffusion equations: solution concepts, regularity, and long-time behavior (2019, methodology): “We refer to [42] for the computation of the Yosida approximation and to [47] for the derivation of (in time) regularized weak formulations.”
General Fractional Integrals and Derivatives with the Sonine Kernels (2021, unknown): “Another example of this type is the following pair of the Sonine kernels ( [27]): κ(t) = hα,ρ(t), ρ ≥ 0, 0 < α < 1, (25)”
The General Fractional Derivative and Related Fractional Differential Equations (2020, background): “In [8,9], the properties of the appropriate defined weak solutions to the linear and quasi-linear evolutionary partial integro-differential equations of second order with the time-operators of type (13) in the form (Dk u)(t) = d dt ∫ t 0 k(t− τ)(u(τ)− u0) dτ, t ∈ R+ (15) were addressed in the case o”
BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER (2009, methodology): “In particular, the global boundedness of appropriately defined weak solutions and a maximum principle for the weak solutions of such equations were established in [25] by employing a different technique compared to the one used in the papers [13], [14].”
Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation (2011, unknown): “In the paper [41], some more general linear and quasilinear evolutionary partial integro-differential equations of second order were investigated.”
Fractional derivatives and the fundamental theorem of fractional calculus (2020, background): “Thus, the many parameters families of the fractional integrals and derivatives (say, the Erdélyi-Kober operators [16] or their Caputo type modifications [22]), the distributed order fractional derivatives [19], the fractional derivatives with the general kernels [17, 32, 33], and the fractional inte”
Fundamental solutions and decay of fully non-local problems (2018, background): “There exists a substantial amount of work on such abstract Volterra and integro-differential equations since the 1970s, in particular on existence and uniqueness, regularity, and long-time behavior of solutions, see, for instance, [8, 14, 31, 32], and the monograph [25].”
Representation of solutions and large-time behavior for fully nonlocal diffusion equations (2015, methodology): “Note that the regularized weak formulation used in [28] and [46] does not involve an integral in time on [0, T ], but it requires the validity of a certain relation pointwise a.”
Operational Calculus for the General Fractional Derivative and Its Applications (2021, unknown): “Another example of this type is the following pair of the Sonine kernels ( [39]): κ(t) = hα,ρ(t), 0 < α < 1, ρ ≥ 0, (9)”