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Hardy type inequalities for $\Delta_{\lambda}$-Laplacians
(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 ...
Hard-type inequalities for $\Delta_{\lambda}$-Laplacians
(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 ...
On the well-posedness of mathematical models for multicomponent biofilms
(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 ...
Attractors met X-elliptic operators
(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 ...
Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications
(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 ...
Attractors for a class of semi-linear degenerate parabolic equations
(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 ...
On the positivity of solutions of systems of stochastic PDEs
(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 ...
Pullback exponential attractors for evolution processes in banach spaces: Theoretical results
(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 ...