Local existence and uniqueness of solutions of a degenerate parabolic system

Abstract

This article deals with a degenerate parabolic system coupled with general nonlinear terms. Using the method of regularization and monotone iteration technique, we obtain the local existence of solutions to the Dirichlet initial boundary value problem. We also establish the uniqueness of the solution if the reaction terms satisfy the Lipschitz condition.

The quenching behavior of a quasilinear parabolic equation with double singular sources

“…Later, Yang, Yin and Jin [14] studied the positive radial solutions to (1.5) in higher dimensional space and got the similar results to [13]. Besides, there are also some other singular properties for nonlinear parabolic equations such as L ∞ blowup and gradient blowup, see the latest papers [7,15,16,20,21] for examples and the references therein. Motivated by the works [8,11,13,18], in this paper, we will study the quenching phenomenon of the more generalized equation (1.1).…”

Stability and superstability of generalized quadratic ternary derivations on non-Archimedean ternary Banach algebras: a fixed point approach

“…In fact, they established stability of Cauchy functional equations over padic fields. After their results some papers (see, for instance, [21][22][23][24][25][26][27]) on the stability of other equations in such spaces have been published. Although different methods are known for establishing the stability of functional equations, almost all proofs depend on Hyers' method in [2].…”