scholarly journals Reconstruction of Source Terms in Evolution Equations by Exact Controllability

1999 ◽  
pp. 143-152
Author(s):  
Masahiro Yamamoto
Keyword(s):  
Evolution Equations ◽  
Exact Controllability ◽  
Source Terms

Maximum entropy principle and classical evolution equations with source terms

2007 ◽  
Vol 374 (2) ◽  
pp. 573-584 ◽  
Author(s):  
J-H. Schönfeldt ◽  
N. Jimenez ◽  
A.R. Plastino ◽  
A. Plastino ◽  
M. Casas
Keyword(s):  
Maximum Entropy ◽  
Evolution Equations ◽  
Maximum Entropy Principle ◽  
Source Terms ◽  
Entropy Principle ◽  
Classical Evolution

scholarly journals Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

2021 ◽  
Vol 5 (3) ◽  
pp. 112
Author(s):  
Azmat Ullah Khan Niazi ◽  
Naveed Iqbal ◽  
Rasool Shah ◽  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon
Keyword(s):  
Differential Equations ◽  
Evolution Equations ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Exact Controllability ◽  
Fractional Evolution Equations ◽  
Liu Process ◽  
Bounded Space ◽  
Fractional Differential ◽  
Derivatives Of

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from the perspective of the Liu process. The class or problems considered here are Caputo fuzzy differential equations with Caputo derivatives of order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt with initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values from U(⊂EN),V(⊂EN) is the other bounded space, and EN represents the set of all upper semi-continuously convex fuzzy numbers on R. In addition, several numerical solutions have been provided to verify the correctness and effectiveness of the main result. Finally, an example is given, which expresses the fuzzy fractional differential equations.

SOME REMARKS ON AFFINE EVOLUTION EQUATIONS WITH APPLICATIONS TO PARTICLE TRANSPORT THEORY

2000 ◽  
Vol 10 (06) ◽  
pp. 877-893 ◽  
Author(s):  
LUIGI BARLETTI
Keyword(s):  
Boundary Conditions ◽  
Banach Spaces ◽  
Particle Transport ◽  
Evolution Equations ◽  
Transport Theory ◽  
Time Dependent ◽  
Source Terms ◽  
Evolution Problems ◽  
Boundary Source ◽  
Transport Problems

We consider evolution problems with time-dependent inhomogeneous boundary conditions and discuss their relations with the theory of inhomogeneous evolution equations in Banach spaces. In the second part of the paper the attention is focused on particle transport problems with time-dependent boundary source terms.

Finite-approximate controllability of fractional evolution equations: variational approach

2018 ◽  
Vol 21 (4) ◽  
pp. 919-936 ◽  
Author(s):  
Nazim I. Mahmudov
Keyword(s):  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Heat Equations ◽  
Natural Conditions ◽  
Finite Dimensional ◽  
Semilinear Evolution Equations

Abstract In this work we extend a variational method to study the approximate controllability and finite dimensional exact controllability (finite-approximate controllability) for the fractional semilinear evolution equations with nonlocal conditions in Hilbert spaces. Assuming the approximate controllability of the corresponding linear equation we obtain sufficient conditions for the finite-approximate controllability of the fractional semilinear evolution equation under natural conditions. The obtained results are generalization and continuation of the recent results on this issue. Applications to heat equations are treated.

scholarly journals Controllability of Impulsive ψ-Caputo Fractional Evolution Equations with Nonlocal Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1358
Author(s):  
Longfei Lin ◽  
Yansheng Liu ◽  
Daliang Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Evolution Equations ◽  
Nonlocal Conditions ◽  
Exact Controllability ◽  
Fractional Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Controllability Result

This paper is mainly concerned with the exact controllability for a class of impulsive ψ-Caputo fractional evolution equations with nonlocal conditions. First, by generalized Laplace transforms, a mild solution for considered problems is introduced. Next, by the Mönch fixed point theorem, the exact controllability result for the considered systems is obtained under some suitable assumptions. Finally, an example is given to support the validity of the main results.

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