Sentence examples for boundary value problems degenerate from inspiring English sources

When (k=0), the three-point boundary value problems degenerate to two-point boundary value problems.

Finally, these results are applied to obtain the maximal regularity properties of the Cauchy problem for a degenerate abstract parabolic equation in mixed (L_{mathbf{p}}) norms, boundary value problems for degenerate integro-differential equations, and infinite systems of degenerate elliptic integro-differential equations.

The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied.

In the works [13, 14], fundamental solutions were found and boundary value problems for degenerate elliptic equations were solved.

Due to applications in gas dynamics, the interest in studying boundary value problems for degenerate elliptic and mixed-type equations with singular coefficients has been growing.

The boundary value problems for singular degenerate arbitrary order differential-operator equations with variable coefficients are considered.

With that in mind, we introduce the notion of a quasi-adjoint state ψ ε to an optimal solution y 0 ∈ W 0 1, p as a solution of the following Dirichlet boundary value problem for degenerate linear elliptic equation: − div ( u θ | ∇ y θ | p − 2 [ I + ( p − 2 ) ∇ y θ | ∇ y θ | ⊗ ∇ y θ | ∇ y θ | ] ∇ ψ θ ) = p div ( | ∇ y θ − ∇ y d | p − 2 ( ∇ y θ − ∇ y d ) ) in  Ω, ψ θ ∈ W 0 1, p , (1.5).

Consideration of a wide range of issues of mathematical physics [1], [2], in particular, the solving of boundary value problems in the heat equation degenerating domains leads to the need to study the singular integral equations of Volterra type when the norm of a integral operator is equal to unit.

We show that blow-up of spatial derivatives of smooth solutions in finite time occurs to initial boundary value problems for a class of degenerate parabolic equations.

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied.

The maximum and antimaximum principles for various boundary value problems are also related with non-degenerate potentials [9 12].