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Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

Kaouther Ammar (2010)

Open Mathematics

The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.

Differential stability of solutions to air quality control problems in urban area

Piotr Holnicki, Jan Sokołowski, Antoni Żochowski (1987)

Aplikace matematiky

The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.

Dirichlet problem for parabolic equations on Hilbert spaces

Anna Talarczyk (2000)

Studia Mathematica

We study a linear second order parabolic equation in an open subset of a separable Hilbert space, with the Dirichlet boundary condition. We prove that a probabilistic formula, analogous to one obtained in the finite-dimensional case, gives a solution to this equation. We also give a uniqueness result.

Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions

Oto Havle, Vít Dolejší, Miloslav Feistauer (2010)

Applications of Mathematics

The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation...

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