We consider a boundary value problem in bounded domain involving degenerate operator of the form L ( u ) = − div x ∇ and suitable nonlinearity f. The function vanishes on smooth 1-codimensional submanifolds Ω where it is not allowed to be C 2 . By using weighted Sobolev spaces we are still able find existence solutions which vanish, trace sense, set vanishes.

In this paper, we develop a static, full-state feedback and a dynamic, output feedback control design framework for continuoustime, multivariable, linear, time-invariant systems subject to time-invariant, sectorbounded, input nonlinearities. The proposed framework directly accounts for robust stability and robust performance over the class of input nonlinearities. Specifically, the problem of f...

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by μ ≤ m ≤ 2M/μK , where μ is the usual chemical potential, M is an intrinsic dimensional scale parameter for the motion of an event in spacetime, and μK is an additional mass potential of the ensemble. For the system including both par...

We prove the existence and uniqueness of a local maximal solution to an H1-critical stochastic wave equation with multiplicative noise on smooth bounded domain D⊂R2 exponential nonlinearity. First, we derive appropriate deterministic Strichartz inequalities in suitable spaces and, then use them arguments based fixed point method show well-posedness result. also present explosion result for cons...

We develop a discrete version of the weak quadratic estimates for operators of type ! of [6], and show that analogous theorems hold. The method is direct and can be generalized to the case of nding necessary and su cient conditions for an operator T to have a bounded functional calculus on a domain which touches (T ) non-tangentially at several points. For operators on L, 1 < p <1, it follows t...

Jones matrix computation is one of the widely used methods in nonlinearitycalculation in laser interferometers. In this paper, the nonlinearity error in developedthree-longitudinal mode heterodyne interferometer (DTLMI) has been mathematicallymodeled at various speeds, by using Jones matrix calculations. This review has been donedespite the fact that simultaneously the main factors including no...

In this paper we study the rate of convergence to complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system equilibria in stoichiometric classes, and whose right hand side is bounded above by quadratic nonlinearity positive orthant. prove similar results on fairly general two-species r...