16 citations · 106 across the 21 of their papers we have counts for
21 papers
Higher Regularity of Time-Periodic Solutions to Nonautonomous Hyperbolic Problems: Away from Resonances
Irina Kmit, Lutz Recke
We study higher regularity and its relation to nonresonant behavior for time-periodic solutions of boundary value problems for one-dimensional linear and nonlinear nonautonomous fi…
An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems
Lutz Recke
We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parame…
A common approach to singular perturbation and homogenization III: Nonlinear periodic homogenization with localized defects
Lutz Recke
We consider periodic homogenization with localized defects for semilinear elliptic equations and systems of the type $$ \nabla\cdot\Big(\Big(A(x/\varepsilon)+B(x/\varepsilon)\Big)\…
Nonlinear non-periodic homogenization: Existence, local uniqueness and estimates
Lutz Recke
We consider periodic homogenization with localized defects of boundary value problems for semilinear ODE systems of the type $$ \Big((A(x/\varepsilon)+B(x/\varepsilon))u'(x)+c(x,u(…
A common approach to singular perturbation and homogenization I: Quasilinear ODE systems
Nikolai N. Nefedov, Lutz Recke
We consider periodic homogenization of boundary value problems for quasilinear second-order ODE systems in divergence form of the type $a(x,x/\varepsilon,u(x),u'(x))'= f(x,x/\varep…
A Common Approach to Singular Perturbation and Homogenization II: Semilinear Elliptic Systems
Nikolai N. Nefedov, Lutz Recke
We consider periodic homogenization of boundary value problems for second-order semilinear elliptic systems in 2D of the type $$ \partial_{x_i}\left(a_{ij}^{αβ}(x/\varepsilon)\part…
Regularity of Time-Periodic Solutions to Autonomous Semilinear Hyperbolic PDEs
Irina Kmit, Lutz Recke
This paper concerns autonomous boundary value problems for 1D semilinear hyperbolic PDEs. For time-periodic classical solutions, which satisfy a certain non-resonance condition, we…
Forced Frequency Locking for Semilinear Dissipative Hyperbolic PDEs
Irina Kmit, Lutz Recke
This paper concerns the behavior of time-periodic solutions to 1D dissipative autonomous semilinear hyperbolic PDEs under the influence of small time-periodic forcing. We show that…
Hopf Bifurcation for General 1D Semilinear Wave Equations with Delay
Irina Kmit, Lutz Recke
We consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type $$ \partial^2_t u(t,x)- a(x,λ)^2\partial_x^2u(t,x)= b(x,λ,u(t,x),u(t-…
Bounded and Almost Periodic Solvability of Nonautonomous Quasilinear Hyperbolic Systems
Irina Kmit, Lutz Recke, Viktor Tkachenko
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming…
Classical Bounded and Almost Periodic Solutions to Quasilinear First-Order Hyperbolic Systems in a Strip
I. Kmit, L. Recke, V. Tkachenko
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in th…
Exponential Dichotomy for Hyperbolic Systems with Periodic Boundary Conditions
R. Klyuchnyk, I. Kmit, L. Recke
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions…
Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs
Irina Kmit, Lutz Recke
In the first part we present a generalized implicit function theorem for abstract equations of the type . We suppose that is a solution for and that $F(λ,\cdo…
Time-Periodic Second-Order Hyperbolic Equations: Fredholmness, Regularity, and Smooth Dependence
Irina Kmit, Lutz Recke
The paper concerns the general linear one-dimensional second-order hyperbolic equation $$ \partial^2_tu - a^2(x,t)\partial^2_xu + a_1(x,t)\partial_tu + a_2(x,t)\partial_xu + a_3(x,…
Robustness of Exponential Dichotomies of Boundary-Value Problems for General First-Order Hyperbolic Systems
I. Kmit, L. Recke, V. Tkachenko
We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed…
Periodic Solutions to Dissipative Hyperbolic Systems. II: Hopf Bifurcation for Semilinear Problems
I. Kmit, L. Recke
We consider boundary value problems for semilinear hyperbolic systems of the type $$ \partial_tu_j + a_j(x,\la)\partial_xu_j + b_j(x,\la,u) = 0, \; x\in(0,1), \;j=1,\dots,n $$ with…
Frequency locking by external forcing in systems with rotational symmetry
Lutz Recke, Anatoly Samoilenko, Viktor Tkachenko +1
We study locking of the modulation frequency of a relative periodic orbit in a general -equivariant system of ordinary differential equations under an external forcing of modu…
Periodic Solutions to Dissipative Hyperbolic Systems. I: Fredholm Solvability of Linear Problems
I. Kmit, L. Recke
This paper concerns linear first-order hyperbolic systems in one space dimension of the type $$ \partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t)…
Frequency locking of modulated waves
Lutz Recke, Anatoly Samoilenko, Alexey Teplinsky +2
We consider the behavior of a modulated wave solution to an -equivariant autonomous system of differential equations under an external forcing of modulated wave type.…
Fredholmness and Smooth Dependence for Linear Time-Periodic Hyperbolic System
Irina Kmit, Lutz Recke
This paper concerns linear one-dimensional hyperbolic systems of the type $$ \partial_tu_j + a_j(x)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x)u_k = f_j(x,t),\; j=1,...…
Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems
Irina Kmit, Lutz Recke
This paper concerns hyperbolic systems of two linear first-order PDEs in one space dimension with periodicity conditions in time and reflection boundary conditions in space. The co…