«Wave packets» sur les groupes nilpotents
Weak periodic solutions of the boundary value problem for nonlinear heat equation
The paper deals with the existence of periodic solutions of the boundary value problem for nonlinear heat equation, where various types of nonlinearities are considered. The proofs are based on the investigation of Liapunov-Schmidt bifurcation system via Leray-Schauder degree theory.
Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces
In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces.
Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law if and if , , depending on the model for the heat flux.
Weak-element Approximations to Elliptic Differential Equations.
Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems
Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.
Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system
The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the weak-strong uniqueness result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists, then a weak solution emanating from the same data coincides with the strong solution on its whole life span. The proof of given assertion relies on a form of a relative entropy...
Weighted energy-dissipation functionals for gradient flows
We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
Weighted energy-dissipation functionals for gradient flows
We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
Weighted Rellich inequality on -type groups and nonisotropic Heisenberg groups.
Well posedness under Levi conditions for a degenerate second order Cauchy problem
Well-posedness for a class of non-Newtonian fluids with general growth conditions
The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-law-type rheology. We describe the growth conditions with...
Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
Zentrale Distributionen auf Exponentialgruppen.
Zum Marx-Shiffmanschen Variationsproblem.
Zur Existenz und Charakterisierung von Bergman-Operatoren. II. Paare von Zugeordneten.
Zur Existenz und Charakterisierung von Bergman-Operatoren. I. Der eingliedrige Lösungsansatz.
Zur Konstruktion gewisser Integraloperatoren für partielle Differentialgleichungen Teil II.
Zur Konstruktion gewisser Integraloperatoren für partielle Differentialgleichungen Teil I.
Zur Unlösbarkeit linearer partieller Differentialgleichungen.