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On a class of retarded integro-differential equations with nonlocal initial conditions [PDF]
Computers & Mathematics with Applications, 2010 The paper deals with the local existence and uniqueness of a mild solution for the Cauchy problem formed by a fractional integro-differential equation with time-delay and a nonlocal initial condition: \[ u'(t) - \int_0^t \frac{(t-s)^{\mu -2}}{\Gamma(\mu -1)} Au(s)ds = F(t,u(t),u(\kappa(t))),\quad t\geq 0; \] \[ u(t) + H_t(u) = \phi(t),\quad-\tau \leq t
Rong-Nian Wang, De-Han Chen
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Журнал Белорусского государственного университета: Математика, информатика, 2018 We consider a nonlinear nonlocal parabolic equation ut = Δu + a(x,t)ur∫Ωup(y,t)dy - b(x,t)uq for (x,t) ∈ Ω × (0,+∞) with nonlinear nonlocal boundary condition u(x,t)|∂Ω × (0,+∞) = ∫Ωk(x,y,t)ul(y,t)dy and initial data u(x,0) = u0(x), x ∈ Ω, where r, p, q,
Alexander L. Gladkov +1 more
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Nonlocal problems for hyperbolic equations with degenerate integral conditions [PDF]
Electronic Journal of Differential Equations, 2016 In this article, we consider a problem for hyperbolic equation with standard initial data and nonlocal condition. A distinct feature of this problem is that the nonlocal second kind integral condition degenerates and turns into a first kind.
Ludmila S. Pulkina
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A nonlocal mixed semilinear problem for second-order hyperbolic equations [PDF]
Electronic Journal of Differential Equations, 2003 In this work we study a nonlinear hyperbolic one-dimensional problem with a nonlocal condition. We establish a blow up result for large initial data and a decay result for small initial data.
Said Mesloub, Salim A. Messaoudi
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Properties of solutions for a reaction–diffusion equation with nonlinear absorption and nonlinear nonlocal Neumann boundary condition [PDF]
Boundary Value Problems, 2018 In this paper, the authors consider the reaction–diffusion equation with nonlinear absorption and nonlinear nonlocal Neumann boundary condition. They prove that the solution either exists globally or blows up in finite time depending on the initial data,
Jian Wang, Hui Yang
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Abstract fractional integro-differential equations involving nonlocal initial conditions in
Advances in Difference Equations, 2011 In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup ...
Wang Rong-Nian, Liu Jun, Chen De-Han
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On the nonlocal problems in time for subdiffusion equations with the Riemann-Liouville derivatives [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 Initial boundary value problems with a time-nonlocal condition for a subdiffusion equation with the Riemann-Liouville time-fractional derivatives are considered.
R.R. Ashurov, Yu.E. Fayziev
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Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions [PDF]
Advances in Difference Equations, 2011 The authors study the existence and uniqueness of mild solutions for the Cauchy problem for impulsive Riemann-Liouville integro-differential equations involving non-local initial condition: \[ \begin{gathered} u'(t)- \int^t_0 {(t- s)^{\alpha-2}\over \Gamma(\alpha- 1)} Au(s)\,ds= F(t,u(t)),\quad 0\leq t\leq a,\;t\neq t_1,\\ u(0)= H(u),\\ u(t^+_i)= u(t ...
Jun Xia, Rong-Nian Wang
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Integrodifferential evolution systems with nonlocal initial conditions [PDF]
Studia Universitatis Babes-Bolyai Matematica, 2020 The paper deals with systems of abstract integrodifferential equations subject to general nonlocal initial conditions. In order to allow the nonlinear terms of the equations to behave independently as much as possible, we use a vector approach based on matrices, vector-valued norms and a vector version of Krasnoselskii's fixed point theorem for a sum ...
Sylvain Koumla, Radu Precup
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On a Class of Multitime Evolution Equations with Nonlocal Initial Conditions [PDF]
Abstract and Applied Analysis, 2007 The existence and uniqueness of the strong solution for a multitime evolution equation with nonlocal initial conditions are proved. The proof is essentially based on a priori estimates and on the density of the range of the operator generated by the considered problem.
Fairouz Zouyed +2 more
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