Now showing items 1-8 of 8

    • Attractors for a class of semi-linear degenerate parabolic equations 

      Kogoj, A.E.; Sonner, S. (2013-12-31)
      We consider degenerate parabolic equations of the form ∂tu = Δλu + f(u) u{pipe}∂Ω = 0, u{pipe}t=0 = u0 in a bounded domain Ω ⊂N, where Δλ is a subelliptic operator of the type (Formula presented.) We prove global existence ...
    • Attractors met X-elliptic operators 

      Kogoj, A.E.; Sonner, S. (2014-12-31)
      We consider degenerate parabolic and damped hyperbolic equations involving an operator L, that is X-elliptic with respect to a family of locally Lipschitz continuous vector fields X={X1,... Xm}. The local well-posedness ...
    • Hard-type inequalities for $\Delta_{\lambda}$-Laplacians 

      Kogoj, A.E.; Sonner, S. (2015-12-31)
      We derive Hardy-type inequalities for a large class of sub-elliptic operators that belong to the class of (Formula presented.) -Laplacians and find explicit values for the constants involved. Our results generalize previous ...
    • Hardy type inequalities for $\Delta_{\lambda}$-Laplacians 

      Kogoj, A.E.; Sonner, S. (2016-01-01)
      We derive Hardy-type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_{\lambda}$-Laplacians and find explicit values for the constants involved. Our results generalize previous ...
    • On the positivity of solutions of systems of stochastic PDEs 

      Cresson, J.; Efendiev, M.A.; Sonner, S. (2013-12-31)
      We study the positivity of solutions of a class of semi-linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit ...
    • On the well-posedness of mathematical models for multicomponent biofilms 

      Sonner, S.; Efendiev, M.A.; Eberl, H.J. (2015-12-31)
      Bacterial biofilms are microbial depositions on immersed surfaces. Their mathematical description leads to degenerate diffusion-reaction equations with two non-Fickian effects: (i) a porous medium equation like degeneracy ...
    • Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications 

      Carvalho, A.N.; Sonner, S. (2014-12-31)
      This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its ...
    • Pullback exponential attractors for evolution processes in banach spaces: Theoretical results 

      Carvalho, A.N.; Sonner, S. (2013-12-31)
      We construct exponential pullback attractors for time continuous asymptotically compact evolution processes in Banach spaces and derive estimates on the fractal dimension of the attractors. We also discuss the corresponding ...