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Local attractivity in nonautonomous semilinear evolution equations

100%

Blot J., Buşe C., Cieutat P.

Nonautonomous Dynamical Systems

2014

tom 1

nr 1

We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity

Nonautonomous partial functional differential equations; existence and regularity

86%

Kpoumiè M. E.-K., Ezzinbi K., Békollè D.

Nonautonomous Dynamical Systems

2017

tom 4

nr 1

108-127

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 conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring the existence of the strict solutions. Finally, we consider a reaction diffusion equation with delay to illustrate the obtained results.

Ograniczanie wyników

2 Nonautonomous Dynamical Systems

1 Blot J.

1 Buşe C.

1 Békollè D.

1 Cieutat P.

1 Ezzinbi K.

1 Kpoumiè M. E.-K.

1 2017

1 2014

Wyniki wyszukiwania

Local attractivity in nonautonomous semilinear evolution equations

Nonautonomous partial functional differential equations; existence and regularity