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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Differential Equations

Differential Equations

Yamoto, Jake

Paperback

Algebra

Currently unavailable to order

ISBN10: 3639065255
ISBN13: 9783639065251
Publisher: Blues Kids Of Amer
Published: Apr 28 2010
Pages: 68
Weight: 0.25
Height: 0.16 Width: 6.00 Depth: 9.00
Language: English
This thesis is mainly concerned about properties of the so-called Filippov operator that is associated with a differential inclusion x(t) ∈ F(t) .e. t ∈ [0, T, where F: Rn is given set-valued map. The operator F produces a new set-valued map F [F ], which in effect regularizes F so that F [F ] has nicer properties. After presenting its definition, we show that F [F ] is always upper-semicontinuous as a map from Rn to the metric space of compact subsets of Rn endowed with the Hausdorffmetric. Our main approach is to study the operator via its support function, which we show is an upper semicontinuous function. We show that the support function can be used to characterize the operator, and prove a new result that characterizes those set-valued maps that are fixed by F; this result was previously known to hold only in dimension one. We also generalize to higher dimensions a known result that characterizes those set-valued maps that are almost everywhere singleton-valued (that is, F (x) = {f (x)} where f: Rn → Rn is an ordinary function).

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