In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in drift and diffusion terms term). particular, solve open question posed by S. Tang X. Zhang, 2009. We propose a new twist on classical strategy for controlling linear systems. By employing refined Carleman estimate, obt...

Abstract Maximal parabolic $L^p$-regularity of linear equations on an evolving surface is shown by pulling back the problem to initial and studying maximal a fixed surface. By freezing coefficients in at time utilizing perturbation argument around freezed time, it that backward difference discretizations along characteristic trajectories can preserve discrete setting. The result applied prove s...

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We use the shadowing approach to study the long-time behavior of numerical approximations of semilinear parabolic equations. We show that the corresponding nonlinear semigroup has a Lipschitz shadowing property in a neighborhood of its global attractor. The proof is based on reduction to an inertial manifold and application of shadowing techniques developed for nite-dimensional systems. When ap...

In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the biparabolic elliptic bi-hyperbolic mixed type partial differential equation of second order. In the present paper some boundary-value problems with non-local initial condition for model and degenerate parabol...

The global-in-time existence of nonnegative solutions to a parabolic strongly coupled system with mixed Dirichlet-Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Writt...