Abstract. This paper is concerned with the the asymptotic behavior of solutions of the critical generalized Korteweg-de Vries equation in a bounded interval with a localized damping term. Combining multiplier techniques and compactness arguments it is shown that the problem of exponential decay of the energy is reduced to prove the unique continuation property of weak solutions. A locally unifo...

We define the family of locally path-bounded digraphs, which is a class of infinite digraphs, and show that on this class it is relatively easy to compute an optimal strategy (winning or nonlosing); and realize a win, when possible, in a finite number of moves. This is done by proving that the Generalized Sprague-Grundy function exists uniquely and has finite values on this class.

We study a class of generalized porous media type flux limited diffusion equations and we prove the existence and uniqueness of entropy solutions. We compute the Rankine-Hugoniot condition on the jump set for solutions which are of locally bounded variation in space and time. We give also a geometric characterization of the entropy conditions on the jump set for a restricted class of this type ...

In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems −div(φ(|∇u|)∇u)− b(u)u ∈ λ∂F (x, u) in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded domain, N ≥ 2 and ∂F (x, u) is a generalized gradient of F (x, t) with respect to t. The main tools utilized are Variational Methods for Locally Lipschitz Functional and a Concentration Compactness T...

Let X be a (connected and reduced) complex space. A qcollar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions) hypersurfaces. Finiteness and vanishing cohomology theorems obtained in [17], [18] for semi q-coronae are generalized in this context and lead to results on extension...

In this paper, we prove two main results. The first one is to give a new condition for the existence of two-parameter p, q-variation path integrals and dominated convergence results for both the one-parameter and two-parameter integrals. Our condition of locally bounded p, q-variation is more natural and easy to verify than those of Young. This result can be easily generalized to multi-paramete...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...