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Displaying similar documents to “Differentiability of weak solutions of nonlinear second order parabolic systems with quadratic growth and nonlinearity q 2

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

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Let Ω be a bounded open subset of n , n > 2 . In Ω we deduce the global differentiability result u H 2 ( Ω , N ) for the solutions u H 1 ( Ω , n ) of the Dirichlet problem u - g H 0 1 ( Ω , N ) , - i D i a i ( x , u , D u ) = B 0 ( x , u , D u ) with controlled growth and nonlinearity q = 2 . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.

On an over-determined problem of free boundary of a degenerate parabolic equation

Jiaqing Pan (2013)

Applications of Mathematics

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This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants K and T 0 , to decide the initial value u 0 such that the solution u ( x , t ) satisfies sup x H u ( T 0 ) | x | K , where H u ( T 0 ) = { x N : u ( x , T 0 ) > 0 } . In this paper, we first establish a priori estimate u t C ( t ) u and a more precise Poincaré type...

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.