Application of Moser's method to a certain type of evolution equations
Solution semigroup and invariant manifolds for functional equations with infinite delay
It is proved that parabolic equations with infinite delay generate -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
Remark on a Newton-Moser type method
Periodic solutions of the equation
The Hopf bifurcation theorem for parabolic equations with infinite delay
The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
Local center manifold for parabolic equations with infinite delay
The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.
Non-standard applications of the Łojasiewicz-Simon theory: Stabilization to equilibria of solutions to phase-field models
This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.
A remark on small divisors problems
Factorization in the algebra of rapidly decreasing functions on
Time-periodic solutions of telegraph equations in spatial variables
Continuous dependence for semilinear parabolic functional equations without uniqueness
An existence theorem for semilinear functional parabolic equations
On the domain dependence of solutions to the two-phase Stefan problem
We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains converge to a solution of the same problem on a domain where is the limit of in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on .
To the 70th anniversary of birthday of Prof. Nečas
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