Quasilinear parabolic equations with nonlinear monotone boundary conditions. (English) Zbl 0962.35101

Lin, Chin-Yuan

Topol. Methods Nonlinear Anal. 13, No. 2, 235-249 (1999).

The author studies the existence of a unique strong solution for a nonlinear parabolic problem, in which the space variable \(x\in (0,1)\). The basic idea is to regard it as a Cauchy problem in \(L^2(0,1)\), associated with a nonlinear operator, which is maximal monotone provided that some appropriate assumptions are fulfilled. For related results, under more general assumptions, see the recent paper by V.-M. Hokkanen and the reviewer [Math. Sci. Res. Hot-Line 3, No. 4, 1-22 (1999; Zbl 0963.35093)].

Reviewer: Gheorghe Moroşanu (Iaşi)

MSC:

35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35K90	Abstract parabolic equations
47H05	Monotone operators and generalizations

Keywords:

maximal monotone operator; unique strong solution

Citations:

Zbl 0963.35093