Some Common Asymptotic Properties of Semilinear Parabolic, Hyperbolic and Elliptic Equations
نویسنده
چکیده
We consider three types of semilinear second order PDEs on a cylindrical domain Ω × (0,∞), where Ω is a bounded domain in N , N 2. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × (0,∞) is reserved for time t, the third type is an elliptic equation with a singled out unbounded variable t. We discuss the asymptotic behavior, as t → ∞, of solutions which are defined and bounded on Ω× (0,∞).
منابع مشابه
Pseudodifferential Operators And Nonlinear PDE
CONTENTS Introduction. 0. Pseudodifferential operators and linear PDE. §0.1 The Fourier integral representation and symbol classes §0.2 Schwartz kernels of pseudodifferential operators §0.3 Adjoints and products §0.4 Elliptic operators and parametrices §0.5 L 2 estimates §0.6 Gårding's inequality §0.7 The sharp Gårding inequality §0.8 Hyperbolic evolution equations §0.9 Egorov's theorem §0.10 M...
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