Radial and nonradial minimizers for some radially symmetric functionals.
Radial Functions and Regularity of Solutions to the Schrödinger Equation.
Radial minimizer of a -Ginzburg-Landau type functional with normal impurity inclusion.
Radial minimizer of a variant of the -Ginzburg-Landau functional.
Radial minimizers of a Ginzburg-Landau functional.
Radially symmetric solutions of a chemotaxis model in the plane-the supercritical case
The existence, uniqueness and large time behaviour of radially symmetric solutions to a chemotaxis system in the plane ℝ² are studied for the (supercritical) value of mass greater than 8π.
Radiation fields
We study the “hyperboloidal Cauchy problem” for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behavior at the boundary, or with polyhomogeneous initial data. Specifically, we consider nonlinear symmetric hyperbolic systems of a form which includes scalar fields with a nonlinearity, as well as wave maps, with initial data given on a hyperboloid; several of the results proved apply to general space-times admitting conformal...
Random and deterministic perturbations of nonlinear oscillators.
Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise
In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic...
Random data Cauchy problem for supercritical Schrödinger equations
Random homogenization of an obstacle problem
Random walks on graphs with volume and time doubling.
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
Randverteilungen von Nullösungen hypoelliptischer Differentialgleichungen.
Rarefaction waves in nonlocal convection-diffusion equations
We consider a nonlocal convection-diffusion equation , where J is a probability density. We supplement this equation with step-like initial conditions and prove the convergence of the corresponding solutions towards a rarefaction wave, i.e. a unique entropy solution of the Riemann problem for the inviscid Burgers equation.
Rate of approach to a singular steady state in quasilinear reaction-diffusion equations
Reaction-diffusion in nonsmooth and closed domains.
Reaction-diffusion system of equations in non-stationary medium and arbitrary non-smooth domains.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions
Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples
The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.