Perturbed evolution problems with absolutely continuous variation in time and applications

Azzam-Laouir, Dalila; Belhoula, Warda; Castaing, Charles; Marques, Manuel

doi:10.1007/s11784-019-0666-2

Cited by 29 publications

(13 citation statements)

References 16 publications

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“…As mentioned in the introduction, our results may find many applications. In the same vein as in [4,5,15], we may show this for second-order evolution inclusions, relaxation, viscosity in control theory, delay evolution inclusions, Skorohod problems and sweeping processes. For shortness, we will present here only a few new applications.…”

supporting

confidence: 61%

“…evolution problems. Indeed, the effectiveness of Vladimirov's pseudo distance in this respect was also proved in several of the authors' works, such as Kunze-Marques [24] and Azzam et al [5,4]; see also the references therein. The computation and the application of Vladimirov's pseudo distance to specific examples may not always be easy and it may demand more work; this, however, may well be a common feature, as, for instance, Brezis-Haraux function and Vladimirov pseudo distance are not completely unrelated.…”

mentioning

confidence: 72%

“…We point out here that, if F = 0, our results above are equivalent to Theorem 3.1 and Theorem 3.3 in [5], and that, if f = 0, our theorems read as Proof. We combine ideas from the proof of Theorem 3.1 above and Theorem 3.1 in [4].…”

Section: (Hmentioning

confidence: 99%

“…The computation and the application of Vladimirov's pseudo distance to specific examples may not always be easy and it may demand more work; this, however, may well be a common feature, as, for instance, Brezis-Haraux function and Vladimirov pseudo distance are not completely unrelated. With our techniques and/or results, a number of subsidiary classes of problems may be solved and then applied in different studies and fields; these include second-order evolution inclusions, relaxation and viscosity in control theory, variational inequalities, Skorohod problems and sweeping processes, asymptotic theory, etc; cf., say, [26,12,3,29,30,4,5,15,2].…”

mentioning

confidence: 99%

“…Using the tools developed in ([4], Theorem 4.1), we present a useful variant of the preceding theorem.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators

Azzam-Laouir¹,

Belhoula²,

Castaing³

et al. 2020

Evolution Equations &Amp; Control Theory

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In this paper, we study the existence of solutions for evolution problems of the form − du dr (t) ∈ A(t)u(t)+F (t, u(t))+f (t, u(t)), where, for each t, A(t) : D(A(t)) → 2 H is a maximal monotone operator in a Hilbert space H with continuous, Lipschitz or absolutely continuous variation in time. The perturbation f is separately integrable on [0, T ] and separately Lipschitz on H, while F is scalarly measurable and separately scalarly upper semicontinuous on H, with convex and weakly compact values. Several new applications are provided.

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supporting

confidence: 61%

mentioning

confidence: 72%