Displaying similar documents to “A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity.”

Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations

Guo Wang Chen (1994)

Commentationes Mathematicae Universitatis Carolinae

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The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation u t = - A ( t ) u x 4 + B ( t ) u x 2 + g ( u ) x 2 + f ( u ) x + h ( u x ) x + G ( u ) with the initial boundary value conditions u ( - ℓ , t ) = u ( ℓ , t ) = 0 , u x 2 ( - ℓ , t ) = u x 2 ( ℓ , t ) = 0 , u ( x , 0 ) = ϕ ( x ) , or with the initial boundary value conditions u x ( - ℓ , t ) = u x ( ℓ , t ) = 0 , u x 3 ( - ℓ , t ) = u x 3 ( ℓ , t ) = 0 , u ( x , 0 ) = ϕ ( x ) , are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.

Convergence of a method for solving the magnetostatic field in nonlinear media

Jozef Kačur, Jindřich Nečas, Josef Polák, Jiří Souček (1968)

Aplikace matematiky

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For solving the boundary-value problem for potential of a stationary magnetic field in two dimensions in ferromagnetics it is possible to use a linearization based on the succesive approximations. In this paper the convergence of this method is proved under some conditions.

Solutions to a perturbed critical semilinear equation concerning the N -Laplacian in ℝ N

Elliot Tonkes (1999)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the N -Laplacian - Δ N u ≡ - div ( | ∇ u | N - 2 ∇ u ) = e ( x , u ) + h ( x ) in Ω where u ∈ W 0 1 , N ( ℝ N ) , Ω is a bounded smooth domain in ℝ N , N ≥ 2 , e ( x , u ) is a critical nonlinearity in the sense of the Trudinger-Moser inequality and h ( x ) ∈ ( W 0 1 , N ) * is a small perturbation.