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20051103BuchApplications of Differential Calculus to Nonlinear Elliptic Boundary Value Problems with Discontinuous Coefficients Palagachev, Dian K.; Recke, Lutz; Softova, Lubomira G.We deal with Dirichlet's problem for second order quasilinear nondivergence form elliptic equations with discontinuous coefficients. First we state suitable structure, growth, and regularity conditions ensuring solvability ...

20110811BuchBoundary Layer Solutions to Problems with Infinite Dimensional Singular and Regular Perturbations Recke, Lutz; Omel'chenko, OlehWe prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed equations of the type $(\varepsilon(x)^2 u'(x))'=f(x,u(x))+ g(x,u(x),\varepsilon(x) u'(x)), 0< x

20110811BuchBoundary Layer Solutions to Singularly Perturbed Problems via the Implicit Function Theorem Omel'chenko, Oleh; Recke, LutzWe prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed problems of the type $\varepsilon^2 u''=f(x,u,\varepsilon u',\varepsilon), 0< x

20210520ZeitschriftenartikelBounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems Kmit, Irina; Recke, Lutz; Tkachenko, ViktorThe paper concerns boundary value problems for general nonautonomous firstorder quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the righthand sides are small. In ...

20210604ZeitschriftenartikelHopf Bifurcation for General 1D Semilinear Wave Equations with Delay Kmit, Irina; Recke, LutzWe consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type ∂2tu(t,x)−a(x,λ)2∂2xu(t,x)=b(x,λ,u(t,x),u(t−τ,x),∂tu(t,x),∂xu(t,x)),x∈(0,1) with smooth coefficient functions ...

20060802BuchInternal Layer Solutions in Quasilinear IntegroDifferential Equations Nefedov, N.N.; Omelchenko, O.E.; Recke, LutzThe Dirichlet boundary value problem for a class of singularly perturbed quasilinear integrodifferential equations is considered. The asymptotic expansion for a new class of solutions, which have internal layers, is ...

20110811BuchMoving Fronts in IntegroParabolic ReactionDiffusionAdvection Equations Nefedov, Nikolai; Nikitin, Andrei; Recke, LutzThe Neumann boundary value problem for a class of singularly perturbed integroparabolic equations is considered. An asymptotic expansion of a new class of solutions of moving front type is constructed, and a theorem of ...

20051020BuchSolvability Properties of Linear Elliptic Boundary Value Problems with Nonsmooth Data Recke, LutzIn this paper linear elliptic boundary value problems of second order with nonsmooth data (L∞coefficients, Lipschitz domain, mixed boundary conditions) are considered. It is shown that the weak solutions are Hölder ...