The decidability of the reachability problem for VASS has been open for a long time, and today the computational complexity of the problem is still open. Obviously, there is more hope of obtaining elementary complexity upper bounds by restricting the class of VASS, for example by considering those for which the reachability sets are effectively semilinear. Presburger arithmetic would then provi...

We calculate the universal Euler characteristic and universal dimension function on semilinear and semibounded sets and obtain some criteria for definable equivalence of semilinear and semibounded sets in terms of these invariants.

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts I, II. In Part I (this pap...

In this paper we study semilinear sets over arbitrary ordered fields. In particular we show that open (resp. closed) semilinear sets are convex if and only if they are basic, that is, a finite intersection of open (resp. closed) halfspaces. As a corollary we get that any bounded convex closed semilinear set is the convex hull of a finite family of points and we obtain a separation result for co...

We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear set are: (i) the maximal value that appears in the vectors of periods and constants and (ii) the number of such sets of periods and constants necessary to de...

The design problem of a high-gain observer is considered for some 2 × and 3 semilinear reaction-diffusion systems, with possibly distinct diffusivities, considering distributed measurement part the state. Due to limitations imposed by parabolic operator, such an observer, infinite-dimensional state transformation first applied map system into more suitable set partial differential equations. th...

Abstract We obtain new concavity results, up to a suitable transformation, for class of quasi-linear equations in convex domain involving the p -Laplace operator and general nonlinearity satisfying concavity-type assumptions. This provides an extension results previously known literature only torsion first eigenvalue equations. In semilinear case <m:math xmlns:m="http://www.w3.org/1998/Math/Mat...

A generalized Cauchy-Kowalevski approach is proposed for flatness-based trajectory planning for boundary controlled semilinear systems of PDEs in a one-dimensional spatial domain. For this, the ansatz presented in [16] using formal integration is generalized towards a unified design framework, which covers linear and semilinear PDEs including rather broad classes of nonlinearities arising in ap...

A generalized Cauchy-Kowalevski approach is proposed for flatness-based trajectory planning for boundary controlled semilinear systems of PDEs in a one-dimensional spatial domain. For this, the ansatz presented in [16] using formal integration is generalized towards a unified design framework, which covers linear and semilinear PDEs including rather broad classes of nonlinearities arising in ap...