An adaptive low-gain integral control framework is developed for tracking constant reference signals in a context of nite-dimensional, asymptotically stable, single-input, single-output linear systems subject to locally Lipschitz, monotone input and output nonlinearities of a general nature: the input nonlinearity is required to satisfy an asymptotic growth condition (of suucient generality to ...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 4 January 2021Accepted: 06 July 2021Published online: 04 November 2021Keywordsnumerical homogenization, multiscale elliptic problem, monotone nonlinearity, $p$-Laplacian, regularization, sparse updatingAMS Subject Headings65N99Publication DataISSN (print): 1540-3459ISSN (...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

It is proved that the stochastic porous media equation in a bounded domain of R, with multiplicative noise, with a monotone nonlinearity of polynomial growth has a unique nonnegative solution in H−1 (in particular is nonnegative measure-valued), provided the initial data is in H−1 and nonnegative. AMS subject Classification 2000: 76S05, 60H15.

We study heteroclinic standing waves (dark solitons) in discrete nonlinear Schrödinger equations with defocussing nonlinearity. Our main result is a quite elementary existence proof for waves with monotone and odd profile, and relies on minimizing an appropriately defined energy functional. We also study the continuum limit and the numerical approximation of standing waves.

We establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation (−∆)u = f(u) in R. Our energy estimates hold for every nonlinearity f and are sharp since they are optimal for one-dimensional solutions, that is, for solutions depending only on one Euclidian variable. As a consequence, in dimen...

This paper introduces the class of K-linear filters, which are linear when restricted to a specified cone K of input sequences, but which can exhibit very nonlinear behavior for input sequences that do not belong to this set. An important special case is the class of monotone-linear filters, which are linear when restricted to monotone input sequences. It is shown that all positive L-filters be...

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in Lp spaces .

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in Lp spaces.