Dynamics of viscous shocks is considered in the modular Burgers equation, where time evolution becomes complicated due to singularities produced by nonlinearity. We prove that are asymptotically stable under odd and general perturbations. For perturbations, proof relies on reduction equation a linear diffusion half-line. developed converting time-evolution problem system equations coupled with ...

In this paper, we consider the Cauchy problem for semilinear $\sigma$-evolution models with an exponential decay memory term. Concerning corresponding linear problem, derive some regularity-loss-type estimates of solutions and generalized diffusion phenomena. Particularly, obtained estimations are sharper than those in previous paper [20]. Then, determine critical exponents power nonlinearity s...

Although integral and differential nonlinearity may not be the most important parameters for high-speed, high dynamic performance data converters, they gain significance when it comes to highresolution imaging applications. The following application note serves as a refresher course for their definitions and details two different, yet commonly used techniques to measure INL and DNL in highspeed...

This article presents and analyzes an approximated exponential integrator for the (inhomogeneous) stochastic Manakov system. system of SPDE occurs in study pulse propagation randomly birefringent optical fibers. For a globally Lipschitz-continuous nonlinearity, we prove that strong order time is $ 1/2 $. then used to has convergence probability almost sure 1/2^{-} $, case cubic nonlinear coupli...

We prove that every finite Borel measure \( \mu \) in \mathbb R^N is bounded from above by the Hausdorff \mathcal{H}^s can be split countable many parts \mu{\lfloor_{_{{E_k}}}} are content \mathcal{H}^s_\infty \). Such a result generalises theorem due to R. Delaware says any set with decomposed as disjoint union of straight sets. apply this decomposition give simpler proof for existence solutio...

The ultimate goal of this study is to develop a numerically effective approximation technique acquire numerical solutions the integer and fractional-order Bratu singular Lane–Emden-type problems especially with exponential nonlinearity. Both initial boundary conditions were considered fractional derivative being in Liouville–Caputo sense. In direct approach, generalized Bessel matrix method bas...

<p style='text-indent:20px;'>This article is a comparative study on an initial-boundary value problem for class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called Sobolev-Galpern type equations. The purpose this work to reveal influence degree source nonlinearity well-posedness solution. By considering four different types nonlinearities, we derive...

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions a plasma. It differs from (VP) for that Poisson coupling has an exponential nonlinearity creates several mathematical difficulties. In particular, while global well-posedness 3 D well understood electron case, this problem remained completely open ion electrons. aim paper fil...

Continuous stirring tank reactors are widely used in the chemical production process, which is always accompanied by nonlinearity, time delay, and uncertainty. Considering characteristic of actual reaction continuous reactors, fault detection problem studied terms T-S fuzzy model. Through a filter performance analysis, sufficient condition for filtering error dynamics obtained, meets exponentia...