Quasilinear parabolic equations with nonlinear monotone boundary conditions
Copyright policy )Quasilinear parabolic equations with nonlinear monotone boundary conditions
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 \textit{V.-M. Hokkanen} and the reviewer [Math. Sci. Res. Hot-Line 3, No. 4, 1-22 (1999; Zbl 0963.35093)].
- National Central University Taiwan
unique strong solution, Abstract parabolic equations, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, General existence and uniqueness theorems (PDE), Monotone operators and generalizations, maximal monotone operator
unique strong solution, Abstract parabolic equations, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, General existence and uniqueness theorems (PDE), Monotone operators and generalizations, maximal monotone operator
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