Regularity of the solutions to quasi-linear parabolic systems with the singular coefficients
DOI:
https://doi.org/10.31926/but.mif.2024.4.66.2.17Keywords:
Leray-Schauder method, semigroup, quasi-linear partial differential equations, nonlinear partial differential equations, nonlinear operator, weak solution, a priori sstimationsAbstract
This article establishes the regularity properties of solutions to the parabolic quasilinear parabolic systems in the divergent form
∂/∂t⃗u, −d/dxi⃗ai (x, t, ⃗u, ∇⃗u) +⃗b (x, t, ⃗u, ∇⃗u) = 0,
under rather general conditions on its coefficients. To prove solvability, we apply the Leray-Schauder theory and method of apriori estimations.
