Displaying similar documents to “Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary p -summable right-hand side”

Existence of weak solutions to doubly degenerate diffusion equations

Aleš Matas, Jochen Merker (2012)

Applications of Mathematics

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We prove existence of weak solutions to doubly degenerate diffusion equations u ˙ = Δ p u m - 1 + f ( m , p ≥ 2 ) by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains Ω ⊂ ℝ n with Dirichlet or Neumann boundary conditions. The function f can be an inhomogeneity or a nonlinearity involving terms of the form f ( u ) or div ( F ( u ) ) . In the appendix, an introduction to weak...

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.