Browsing 1 - Oberwolfach Preprints (OWP) by MSC "35"
Now showing items 1-10 of 10
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The algebra of differential operators for a Gegenbauer weight matrix
[OWP-2015-07] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)In this work we study in detail the algebra of differential operators $\mathcal{D}(W)$ associated with a Gegenbauer matrix weight. We prove that two second order operators generate the algebra, indeed $\mathcal{D}(W)$ is ... -
An Extension Problem and Trace Hardy Inequality for the Sublaplacian on H-Type Groups
[OWP-2017-20] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-24)In this paper we study the extension problem for the sublaplacian on a H-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian. -
Global Solutions to Stochastic Wave Equations with Superlinear Coefficients
[OWP-2019-26] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-13)We prove existence and uniqueness of a random field solution $(u(t,x);(t,x)\in [0,T]\times \mathbb{R}^d)$ to a stochastic wave equation in dimensions $d=1,2,3$ with diffusion and drift coefficients of the form $|x| ... -
Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary
[OWP-2018-06] (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-16)We consider a domain $\Omega_\varepsilon\subset\mathbb{R}^N$, $N\geq2$, with a very rough boundary depending on~$\varepsilon$. For instance, if $N=3$ the domain $\Omega_\varepsilon$ has the form of a brush with an ... -
Review of the Methods of Reflections
[OWP-2017-27] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-18)The methods of reflections were invented to obtain approximate solutions of the motion of more than one particle in a given environment, provided that one can represent the solution for one particle rather easily. This ... -
Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay
[OWP-2007-12] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-28)We study positive bounded wave solutions $u(t, x) = \phi(\nu \cdot x+ct)$, $\phi(-\infty)=0$, of equation $u_t(t, x)=\delta u(t,x)−u(t,x) +g(u(t−h,x))$, $x \in \mathbb{R}^m$(*). It is supposed that Eq. (∗) has exactly two ... -
Some Results Related to Schiffer's Problem
[OWP-2018-18] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-16)We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain $\Omega$ with analytic boundary $\partial\Omega$ having at least one bounded connected component \begin{eqnarray*} ... -
Spatial-Skin Effect for a Spectral Problem with "Slightly Heavy" Concentrated Masses in a Thick Cascade Junction
[OWP-2012-10] (Mathematisches Forschungsinstitut Oberwolfach, 2012-07-03)The asymptotic behavior (as $\varepsilon \to 0$) of eigenvalues and eigenfunctions of a boundary- value problem for the Laplace operator in a thick cascade junction with concentrated masses is studied. This cascade junction ... -
Time Discretization Schemes for Hyperbolic Systems on Networks by ε-Expansion
[OWP-2019-03] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-12)We consider partial differential equations on networks with a small parameter $\epsilon$, which are hyperbolic for $\epsilon>0$ and parabolic for $\epsilon=0$. With a combination of an $\epsilon$-expansion and Runge-Kutta ... -
A Well-Posedness Result for Viscous Compressible Fluids with Only Bounded Density
[OWP-2018-10] (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-28)We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and ...