On properties of solutions to boundary value and extremum problems for nonlinear reaction--diffusion--convection equation
On properties of solutions to boundary value and extremum problems for nonlinear reaction--diffusion--convection equation
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 22, 2, стр. 1599-1613 (2025)
Abstract:
The local existence and uniqueness of a strong solution to inhomogeneous boundary value problem for the reaction--diffusion--convection equation with variable coefficients is proved and its apriory estimate is obtained. For the boundary value problem under consideration, a control problem
is studied for which an optimality system is derived.
Keywords: nonlinear reaction--diffusion--convection equation, variable coefficients, weak solution, maximum principle, strong solution, control problem, extremum problem, optimality system