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math.CA2023
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…
math.AP2023
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…
math.AP2023
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…