This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform...

We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution i...

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type-I and type-II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen’s model. The nonlinearity is coming f...

The evolution of a magnetoelastic material is described by a nonlinear hyperbolic-parabolic system. We introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem. On a hyperbolic-parabolic system arising in magnetoelasticity M. Chipot∗ I. Shafrir† V. Valente ‡ G. Vergara Caffarelli§ November 6, 2007 keywords: Magn...

The paper is concerned with Lp error analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron ...

Representation of functionals of non-Markov processes is studied for bounded and unbounded domains. These functionals are represented via solutions of backward parabolic Ito equations. This results is based on an analog of the second fundamental inequality and the related existence theorem are obtained for backward parabolic Ito equations. AMS 1991 subject classification: Primary 60J55, 60J60, ...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

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...