Journal: Journal of Evolution Equations

Abbreviation

J. evol. equ.

Publisher

Birkhäuser

Journal Volumes

ISSN

1424-3199
1424-3202

Description

Filters

2010 - 201922020 - 20233
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Publications 1 - 5 of 5
  • A perturbation result for semi-linear stochastic differential equations in UMD Banach spaces
    Item type: Journal Article
    Cox, Sonja Gisela; Hausenblas, Erika (2013)
    Journal of Evolution Equations
  • The time-dependent Hartree-Fock-Bogoliubm equations for Bosons
    Item type: Journal Article
    Bach, Volker; Breteaux, Sebastien; Chen, Thomas; et al. (2022)
    Journal of Evolution Equations
    We introduce the map of dynamics of quantum Bose gases into dynamics of quasifree states, which we call the "nonlinear quasifree approximation". We use this map to derive the time-dependent Hartree-Fock-Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose-Einstein condensate. We prove global well-posedness of the I IFB equations for pair potentials satisfying suitable regularity conditions, and we establish important conservation laws. We show that the space of solutions of the HFB equations has a symplectic structure reminiscent of a Hamiltonian system. This is then used to relate the HFB equations to the HFB eigenvalue equations discussed in the physics literature. We also construct Gibbs equilibrium states at positive temperature associated with the HFB equations, and we establish criteria for the appearance of Bose-Einstein condensation.
  • Loss of convexity and embeddedness for geometric evolution equations of higher order
    Item type: Journal Article
    Blatt, Simon (2010)
    Journal of Evolution Equations
  • Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
    Item type: Journal Article
    Cuchiero, Christa; Teichmann, Josef (2020)
    Journal of Evolution Equations
    We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller property which was introduced in, e.g., Dörsek and Teichmann (A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). In particular, we provide new existence, uniqueness and approximation results for Markovian lifts of affine rough volatility models of general jump diffusion type. We demonstrate that in this Markovian light the theory of stochastic Volterra processes becomes almost classical.
  • On the existence and Hölder regularity of solutions to some nonlinear Cauchy–Neumann problems
    Item type: Journal Article
    Audrito, Alessandro (2023)
    Journal of Evolution Equations
    We prove uniform parabolic Hölder estimates of De Giorgi–Nash–Moser type for sequences of minimizers of the functionals Eε(W)=∫0∞e-t/εε{∫R+N+1ya(ε|∂tW|2+|∇W|2)dX+∫RN×{0}Φ(w)dx}dt,ε∈(0,1) where a∈ (- 1 , 1) is a fixed parameter, R+N+1 is the upper half-space and d X= d xd y . As a consequence, we deduce the existence and Hölder regularity of weak solutions to a class of weighted nonlinear Cauchy–Neumann problems arising in combustion theory and fractional diffusion.
Publications 1 - 5 of 5