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Nonlinear Partial Functional Differential Equations: Existence and Stability

Journal of Mathematical Analysis and Applications, 2001
Existence and uniqueness of solutions for a class of nonlinear functional differential equations in Hilbert spaces are established. Sufficient conditions which guarantee the transference of exponential stability from partial differential equations to partial functional differential equations are studied.
Tomáš Caraballo
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Existence and stability for partial functional differential equations [PDF]

Transactions of the American Mathematical Society, 1974
Publisher Summary This chapter discusses the existence and stability for a class of partial functional differential equations. As a model for this class, one may take the equation wt(x, t) = wxx (x, t) + ƒ(t, w(x, t − r)), 0 ≤ x ≤ Π, t ≥ 0, w(0, t) = w(Π, t) = 0, t ≥ 0, w(x, t) = Φ (x, t), 0 ≤ x ≤ Π, −r ≤ t ≤ 0, where ƒ is a linear or nonlinear ...
Travis, C. C., Webb, G. F.
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Oscillation in neutral partial functional differential equations and inequalities

Electronic Journal of Qualitative Theory of Differential Equations, 1998
We derive some sufficient conditions for certain classes of ordinary differential inequalities of neutral type with distributed delay not to have eventually positive or negative solutions.
X. Fu, Jianhong Wu
doaj   +3 more sources

Formulation of the normal form of Turing-Hopf bifurcation in partial functional differential equations

Journal of Differential Equations, 2020
Turing-Hopf bifurcation is considered as an important mechanism for generating complex spatio-temporal patterns in dynamical systems. In this work, the normal form up to the third order for the Hopf-steady state bifurcation, which includes the Turing ...
Weihua Jiang, Junping Shi
exaly   +2 more sources

Invariant manifolds of partial functional differential equations

Journal of Differential Equations, 2004
The authors give a proof for the existence and attractivity of center-unstable, center and stable manifolds for general evolutionary processes using the method of graph transforms. They indicate that their results can be applied to a large class of equations generating evolutionary processes that may not be strongly continuous.
Van Minh, Nguyen, Wu, Jianhong
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Existence, stability, and compactness in the 𝛼-norm for partial functional differential equations [PDF]

Transactions of the American Mathematical Society, 1978
The abstract ordinary functional differential equation ( a / d
Travis, C. C., Webb, G. F.
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Oscillation of Solutions of Neutral Partial Functional Differential Equations

Journal of Mathematical Analysis and Applications, 1999
The authors use the generalized Riccati transformation in order to obtain sufficient conditions for an oscillation of the solutions to the following neutral partial differential-functional equations \[ {\partial \over \partial t}\left[p(t) {\partial\over\partial t}\left(u(x,t)+ \sum^\ell_{i=1} \lambda_i(t) u(x,t-\tau_i) \right)\right] = \] \[ =a(t ...
Li, Wei Nian, Cui, Bao Tong
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On the Partial Equiasymptotic Stability in Functional Differential Equations

Journal of Mathematical Analysis and Applications, 2002
A system of functional-differential equations with delay \(dz/dt=Z(t,z_t)\), where \(Z\) is a vector-valued functional, is considered. It is supposed that this system has a zero solution \(z=0\). Definitions of its partial stability, partial asymptotical stability and partial equiasymptotical stability are given.
exaly   +3 more sources

A Characteristic Equation for Non-autonomous Partial Functional Differential Equations

Journal of Differential Equations, 2002
Using the evolution semigroup approach, the authors give a characterization of exponential stability for the nonautonomous partial functional-differential equation \[ \dot{u}(t) = A(t) u(t) + L(t) u_t,\quad t \geq s, \qquad u(t) = \varphi(t-s),\quad s-r \leq t \leq s, \] in terms of a generalized characteristic equation which is formulated on adequate ...
Gühring, Gabriele, Räbiger, Frank, Schnaubelt, Roland   +2 more
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Nonautonomous partial functional differential equations; existence and regularity

Nonautonomous Dynamical Systems, 2017
Abstract The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the ...
Moussa El-Khalil Kpoumié, Khalil Ezzinbi, David Békollè   +2 more
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