Solvability problem for strong-nonlinear nondiagonal parabolic system

Solvability Problem for Strong-nonlinear Nondiagonal Parabolic System

A class of q-nonlinear parabolic systems with a nondiagonal principal matrix and strong nonlinearities in the gradient is considered.We discuss the global in time solvability results of the classical initial boundary value problems in the case of two spatial variables. The systems with nonlinearities q ∈ (1, 2), q = 2, q > 2, are analyzed.

Solvability for Parabolic Poincaré Problem

Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities II. Local and global solvability results

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...

On Solvability of the Nonlinear Optimal Control Problem for Processes Described by the Semi-linear Parabolic Equations

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...

Solvability for a System of Nonlinear Fractional Higher–order Three–point Boundary Value Problem

Existence of eigenvalues yielding single and multiple positive solutions for a system of higher order fractional differential equations along with boundary conditions is established. The results are obtained by the use of a Guo-Krasnosel’skii fixed point theorem in cones.