Displaying similar documents to “On the center of the generalized Liénard system”

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

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We show a locally uniform bound for global nonnegative solutions of the system u t = Δ u + u v - b u , v t = Δ v + a u in ( 0 , + ) × Ω , u = v = 0 on ( 0 , + ) × Ω , where a > 0 , b 0 and Ω is a bounded domain in n , n 2 . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

On the existence of solutions for some nondegenerate nonlinear wave equations of Kirchhoff type

Jong Yeoul Park, Jeong Ja Bae (2002)

Czechoslovak Mathematical Journal

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Let Ω be a bounded domain in n with a smooth boundary Γ . In this work we study the existence of solutions for the following boundary value problem: 2 y t 2 - M Ω | y | 2 d x Δ y - t Δ y = f ( y ) in Q = Ω × ( 0 , ) , . 1 y = 0 in Σ 1 = Γ 1 × ( 0 , ) , M Ω | y | 2 d x y ν + t y ν = g in Σ 0 = Γ 0 × ( 0 , ) , y ( 0 ) = y 0 , y t ( 0 ) = y 1 in Ω , ( 1 ) where M is a C 1 -function such that M ( λ ) λ 0 > 0 for every λ 0 and f ( y ) = | y | α y for α 0 .

Differentiability of weak solutions of nonlinear second order parabolic systems with quadratic growth and nonlinearity q 2

Luisa Fattorusso (2004)

Commentationes Mathematicae Universitatis Carolinae

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Let Ω be a bounded open subset of n , let X = ( x , t ) be a point of n × N . In the cylinder Q = Ω × ( - T , 0 ) , T > 0 , we deduce the local differentiability result u L 2 ( - a , 0 , H 2 ( B ( σ ) , N ) ) H 1 ( - a , 0 , L 2 ( B ( σ ) , N ) ) for the solutions u of the class L q ( - T , 0 , H 1 , q ( Ω , N ) ) C 0 , λ ( Q ¯ , N ) ( 0 < λ < 1 , N integer 1 ) of the nonlinear parabolic system - i = 1 n D i a i ( X , u , D u ) + u t = B 0 ( X , u , D u ) with quadratic growth and nonlinearity q 2 . This result had been obtained making use of the interpolation theory and an imbedding theorem of Gagliardo-Nirenberg type for functions u belonging to W 1 , q C 0 , λ .