In this paper, we establish the global existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by Brownian motion on a bounded domain D in setting L2(D) space. The result is valid for all initial values contrast existing literature. Sobolev inequality plays an important role.

This paper proposes two model predictive control (MPC) methods for a Hammerstein with both unmeasurable state and bounded disturbance. First, dynamic output feedback MPC is designed such that the dynamics of estimation error decoupled from estimated state. Hence, separation principle holds part controller parameters can be off-line. Second, case considered where nonlinearity not exactly inverte...

We impose in the nonsymmetric gravitational theory, by means of Lagrange multiplier fields in the action, a set of covariant constraints on the antisymmetric tensor field. The canonical Hamiltonian constraints in the weak field approximation for the antisymmetric sector yield a Hamiltonian energy bounded from below. An analysis of the Cauchy evolution, in terms of an expansion of the antisymmet...

In this paper we develop fixed-order (i.e., fulland reduced-order) controllers for systems with actuator amplitude constraints and exogenous bounded energy LZ disturbances. The actuator amplitude saturation and disturbance rejection constraints are embedded within an optimization problem by constructing a Riccati equation whose solution guarantees closed-loop global asymptotic stability in the ...

Infrared, optical, and ultraviolet spectropolarimetry of cosmological sources is used to constrain the pure electromagnetic sector of a general Lorentz-violating standard-model extension. The coefficients for Lorentz violation are bounded to less than 3 x 10(-32).

This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of convolution type nonlinearity tends critical one in sense Hardy–Littlewood–Sobolev inequality, we obtain existence multiple positive solutions via Lusternik–Schnirelmann category and nonlocal global compactness. Moreover, prove that topology domain furnishes ...

We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem −∆u + K(x)g(u) + |∇u| a = λf (x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R N (N ≥ 2) is a smooth bounded domain, 0 < a ≤ 2, λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlin...

This paper presents a continuous-time adaptive control scheme for systems with uncertain nonsymmetrical deadzone nonlinearity located at the output of a plant. An adaptive inverse function is developed and used in conjunction with a robust adaptive controller to reduce the effect of deadzone nonlinearity. The deadzone inverse function is also implemented in continuous time, and an adaptive upda...

We prove the convergence of an adaptive linear finite element method for computing eigenvalues and eigenfunctions of second order symmetric elliptic partial differential operators. The weak form is assumed to yield a bilinear form which is bounded and coercive in H1. Each step of the adaptive procedure refines elements in which a standard a posteriori error estimator is large and also refines e...

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...