Fuzzy Differential Inclusion: An Application to Epidemiology

2004 ◽  
pp. 631-637 ◽  
Author(s):  
Laécio C. Barros ◽  
Rodney C. Bassanezi ◽  
Renata Z. G. Oliveira
Keyword(s):  
Differential Inclusion

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Lipschitzian Function ◽  
The Clarke Subdifferential

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

scholarly journals Positive Solvability for Conjugate Fractional Differential Inclusion of (k,n-k) Type without Continuity and Compactness

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 170
Author(s):  
Ahmed Salem ◽  
Aeshah Al-Dosari
Keyword(s):  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Inclusion Type ◽  
Fractional Differential Inclusion ◽  
Fractional Differential

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ>0,1≤k≤n−1.

Filippov lemma for measure differential inclusion

2021 ◽  
Vol 294 (3) ◽  
pp. 580-602
Author(s):  
Andrzej Fryszkowski ◽  
Jacek Sadowski
Keyword(s):  
Differential Inclusion

scholarly journals Rigidity of Branching Microstructures in Shape Memory Alloys

2021 ◽  
Author(s):  
Theresa M. Simon
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Differential Inclusion ◽  
Linearized Strain ◽  
Weak Limits ◽  
All Solutions ◽  
Rank One ◽  
Branched Structures ◽  
Habit Planes

AbstractWe analyze generic sequences for which the geometrically linear energy $$\begin{aligned} E_\eta (u,\chi )\,{:}{=} \,\eta ^{-\frac{2}{3}}\int _{B_{1}\left( 0\right) } \left| e(u)- \sum _{i=1}^3 \chi _ie_i\right| ^2 \, \mathrm {d}x+\eta ^\frac{1}{3} \sum _{i=1}^3 |D\chi _i|({B_{1}\left( 0\right) }) \end{aligned}$$ E η ( u , χ ) : = η - 2 3 ∫ B 1 0 e ( u ) - ∑ i = 1 3 χ i e i 2 d x + η 1 3 ∑ i = 1 3 | D χ i | ( B 1 0 ) remains bounded in the limit $$\eta \rightarrow 0$$ η → 0 . Here $$ e(u) \,{:}{=}\,1/2(Du + Du^T)$$ e ( u ) : = 1 / 2 ( D u + D u T ) is the (linearized) strain of the displacement u, the strains $$e_i$$ e i correspond to the martensite strains of a shape memory alloy undergoing cubic-to-tetragonal transformations and the partition into phases is given by $$\chi _i:{B_{1}\left( 0\right) } \rightarrow \{0,1\}$$ χ i : B 1 0 → { 0 , 1 } . In this regime it is known that in addition to simple laminates, branched structures are also possible, which if austenite was present would enable the alloy to form habit planes. In an ansatz-free manner we prove that the alignment of macroscopic interfaces between martensite twins is as predicted by well-known rank-one conditions. Our proof proceeds via the non-convex, non-discrete-valued differential inclusion $$\begin{aligned} e(u) \in \bigcup _{1\le i\ne j\le 3} {\text {conv}} \{e_i,e_j\}, \end{aligned}$$ e ( u ) ∈ ⋃ 1 ≤ i ≠ j ≤ 3 conv { e i , e j } , satisfied by the weak limits of bounded energy sequences and of which we classify all solutions. In particular, there exist no convex integration solutions of the inclusion with complicated geometric structures.

scholarly journals Sex on the move: Gender, subjectivity and differential inclusion

Subjectivity ◽  
2009 ◽  
Vol 29 (1) ◽  
pp. 389-406 ◽  
Author(s):  
Rutvica Andrijasevic
Keyword(s):  
Differential Inclusion ◽  
Gender Subjectivity
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