Results 211 to 220 of about 3,412 (247)

On the Cauchy Problems of Fractional Evolution Equations with Nonlocal Initial Conditions

Results in Mathematics, 2011
The authors study Cauchy problems with nonlocal conditions involving fractional derivatives. Criteria for compactness and Lipschitz continuity of the nonlocal term are relaxed in order to prove existence and uniqueness of a solution. The compactness of the semigroup is used to relax the conditions on the nonlocal term.
Rong-Nian Wang
exaly   +3 more sources

A class of stochastic nonlocal evolution equations with nonlocal initial conditions

Analysis and Applications, 2023
In this paper, we consider the existence and uniqueness of mild solutions for stochastic nonlocal evolution equations with Lévy diffusion operator and nonlocal initial conditions. Based on the continuity of the Lévy semigroup and the technique of the measure of noncompactness, we establish the local existence of mild solutions in [Formula: see text ...
Yarong Liu, Yejuan Wang, Peter E. Kloeden   +2 more
openaire   +2 more sources

Abstract reaction–diffusion systems with nonlocal initial conditions

Nonlinear Analysis: Theory, Methods & Applications, 2014
The authors study the abstract nonlinear first-order delay reaction-diffusion system with nonlocal initial conditions \[ \begin{aligned} & u'(t) \in Au(t)+f(t,u_{t},v_{t}), \;t\in [ 0,\infty),\\ & v'(t) \in Bv(t)+g(t,u_{t},v_{t}), \;t\in [ 0,\infty),\\ & u(t)=p(u,v)(t), \;t\in [ -\tau ,0],\\ & v(t)=q(u,v)(t), \;t\in [ -\tau ,0],\end{aligned}\tag{1 ...
Burlică, Monica-Dana, Roşu, Daniela, Vrabie, Ioan I.   +2 more
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On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions

Journal of Optimization Theory and Applications, 2008
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Chang, Y.-K., Nieto, J. J., Li, W.-S.
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Regularity for evolution equations with nonlocal initial conditions

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Pengyu, Zhang, Xuping, Li, Yongxiang   +2 more
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Nonlocal initial conditions for fractional diffusion problems

AIP Conference Proceedings, 2017
We discuss the existence and uniqueness of solutions of nonlinear space-fractional diffusion equations subject to an initial condition of integral type. Our approach shall rely on fixed point theorems.We discuss the existence and uniqueness of solutions of nonlinear space-fractional diffusion equations subject to an initial condition of integral type ...
Abdelkader Boucherif, Boumediene Abdellaoui, Tarik Mohamed Touaoula   +2 more
openaire   +1 more source

Existence of Semilinear Differential Equations with Nonlocal Initial Conditions

Acta Mathematica Sinica, English Series, 2006
The author considers the existence of mild solutions for semilinear Cauchy problems \[ u'(t) =Au(t) +f(t,u(t)), \quad t\in [0,b]\text{ a.e., }u(0) =g(u) +u_0, \] where \(A\) is an infinitesimal generator of a strongly continuous semigroup \(T(t)\) of bounded linear operators in a Banach space \(X\), \(f: [0,b] \times X\to X\), \(g\in C([0,b] ;X)\) are ...
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Recovering Sparse Initial Conditions in Nonlocal Diffusion

Journal of Computational Mathematics
This work addresses the inverse problem of recovering sparse initial data in spatial fractional parabolic equations. The associated solution operator for initial-boundary value problem is continuous and compact, implying severe ill-posedness. To overcome this, an $ℓ_1$-regularized formulation is considered.
Jinyan Tian, Fangfang Dou
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Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

Journal of Optimization Theory and Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Y. K. Chang, Juan José Nieto 0001, W. S. Li   +2 more
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Study on Integrodifferential Evolution Systems with Nonlocal Initial Conditions

2021
The work is concerned with systems of abstract integrodifferential equations with general nonlocal initial conditions. To allow the nonlinear terms of the equations to behave as independently as possible, we employ a vector approach based on matrices, vector-valued norms, and a vector version of Krasnoselskii's fixed point theorem for a sum of two ...
Sylvain Koumla, Radu Precup
openaire   +1 more source