Global solvability of Cauchy–Dirichlet problem for fully nonlinear parabolic systems

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

Solvability of monotone systems of fully nonlinear elliptic PDE's

Solvability of uniformly elliptic fully nonlinear PDE

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-BellmanIsaacs type, with unbounded ingredients and quadratic growth in the gradient, without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.

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...