ON THE ASYMPTOTICS OF SOLUTIONS TO A DUAL NONLINEAR REACTION-DIFFUSION PROBLEM WITH A SOURCE AND INHOMOGENEOUS DENSITY
Keywords:
Global solvability, diffusion, inhomogeneous medium, solutions, reference equation, self-similar analysis, solution asymptotics, initial approximation, iterative processAbstract
Recently, there has been a surge in the analysis and modeling of mathematical models of reaction-diffusion. Mathematical models of nonlinear reaction-diffusion are described by nonlinear parabolic equations in partial derivatives. Explicit analytical solutions to such nonlinearly coupled systems of partial differential equations rarely exist, and therefore several numerical methods have been used to obtain approximate solutions. In this work, based on self-similar analysis and the method of standard equations, we study the properties of a nonlinear reaction-diffusion with an initial condition. The qualitative properties of solutions of nonlinear parabolic diffusion equations with initial conditions are investigated. It is proved that for certain values of the numerical parameters of the nonlinear diffusion equation. On the basis of self-similar analysis and the principle of comparison of solutions, a Fujita-type critical exponent and a critical value of global solvability are established. Using the comparison theorem, upper bounds for global solutions and lower bounds for solutions with destruction are obtained.
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