Research and analysis of the solution of Hamilton-Jacobi equation

Relevance of the research work. In addition to the construction of stable differential circuits with nonlinear effects and visualization of the approximate solution using modern computer technologies, linearization methods are also relevant. In mathematical modeling, it was confirmed that the calculation experiment was successful, applying qualitative and analytical methods of automodel and approximateautomodel equations, as well as the theory of special derivative equations. The main aspect and complexity of the studied mathematical models is that the solution is not unique. It is this aspect that distinguishes them from classical problems with a single solution. The scientific novelty of this research work consists in the numerical and analytical study and numerical modeling of the nonlinear mathematical models of the nonlinear heat propagation process expressed by the Hamilton-Jacobi equations.