Anisotropic equations: Uniqueness and existence results

By Stanislav N. Antontsev, Michel Chipot. Differential and Integral Equations, 2008

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in a bounded domain Ω ⊂ R with Lipschitz continuous boundary Γ = ∂Ω. We consider in particular mixed boundary conditions -i.e., Dirichlet condition on one part of the boundary and Neumann condition on the other part. We study also uniqueness of weak solutions for the parabolic equations  ∂tu = ∂xi ( ai(x, t, u) |∂xiu| pi−2 ∂xiu ) + f in Ω× (0, T ), u = 0 on Γ× (0, T ) = ∂Ω× (0, T ), u(x, 0) = u0 x ∈ Ω. It is assumed that the constant exponents pi satisfy 1 < pi < ∞ and the coefficients ai are such that 0 < λ ≤ λi ≤ ai(x, u) < ∞, ∀i, a.e. x ∈ Ω, (a.e. t ∈ (0, T )), ∀u ∈ R. We indicate also conditions which guarantee existence of solutions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/40db2954ccb64fb870ac3b13d1ecea78ddb9a954

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Citations in the corpus

Anisotropic parabolic equations with variable nonlinearity (2009, methodology): “Parabolic Equation with Variable Nonlinearity 357 here to monographs [24], [36], papers [5], [9], [20], [29] and the review paper [30] which provide an excellent insight to the theory of evolutional p-Laplacian equations.”
Vanishing solutions of anisotropic parabolic equations with variable nonlinearity (2010, unknown): “, [1, 2, 3, 13, 15, 16, 18, 19, 20, 26, 27, 30, 31] and the further references therein.”