We consider a semi-linear advection equation driven by a highly-oscillatory space-time Gaussian random field, with the randomness affecting both the drift and the nonlinearity. In the linear setting, classical results show that the characteristics converge in distribution to a homogenized Brownian motion, hence the point-wise law of the solution is close to a functional of the Brownian motion. ...

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described. Let k be a field of characteristic zero containing all ℓ-primary roots of unity for a prime ℓ, F...

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this paper, we deal with linear codes of Fnq invariant under a semi-linear map T : F q → F q for some n ≥ 2. In particular, we study three kind of their dual codes, some relations between them and we focus on codes which are products of module skew codes in the non-commutative polynomial ring as a subca...

We prove local well-posedness results for the semi-linear wave equation for data in H , 0 < < n?3 2(n?1) , extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space X r;p k .

We study the conormal regularity of bounded solutions to semi-linear strictly hyperbolic equations on domains with diiractive boundaries: P u = f (x; u) in X; u @X = 0; u 2 L 1 loc (X): If X ? X and X is the domain of innuence of X ? we consider solutions such that singsupp(u) \ X ? \ @X = ; and further suppose that u X? is conormal with respect to a smooth characteristic hypersurface, the inco...

We consider varieties of pointed lattice-ordered algebras satisfying a restricted distributivity condition and admitting a very weak implication. Examples of these varieties are ubiquitous in algebraic logic: integral or distributive residuated lattices; their {·}-free subreducts; their expansions (hence, in particular, Boolean algebras with operators and modal algebras); and varieties arising ...

We compute general (non-radial) positive solutions of the semi-linear elliptic PDE u + u + u 5 = 0, in 3 space dimensions (where the nonlinearity is critical) using the Finite Element Method. We have overcome two fundamental diiculties in this approach. Firstly the convergence of the numerical solutions is very slow (on regular grids) and it is necessary to work with very ne meshes (10 6 nodes)...