Results 291 to 300 of about 172,917 (327)

ON BISINGULAR INTEGRAL OPERATORS WITH DISCONTINUOUS COEFFICIENTS

Mathematics of the USSR-Sbornik, 1976
Necessary and sufficient conditions are obtained for bisingular integral operators on piecewise smooth Ljapunov curves with discontinuous coefficients in the -spaces with a weight to be Noetherian. The Banach algebra generated by these operators is studied; a regularizer is constructed in the case of continuous coefficients.Bibliography: 40 titles.
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Dynamic bilateral contact with discontinuous friction coefficient

Nonlinear Analysis: Theory, Methods & Applications, 2001
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Kuttler, Kenneth L., Shillor, Meir
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One-dimensional transport equations with discontinuous coefficients

Nonlinear Analysis: Theory, Methods & Applications, 1998
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Bouchut, François, James, François
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Inverse eigenvalue problems with discontinuous coefficients

Inverse Problems, 1988
The direct and the inverse eigenvalue problem on a finite interval for a Sturm-Liouville equation in the so-called impedance form is investigated. The problem is treated for the following regularity conditions on the impedance function p: (i) ln p is of bounded variation; (ii) \(p'/p\) is an \(L^ r\) function, where \(1\leq r\leq \infty\).
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On reconstruction of Kolmogorov operators with discontinuous coefficients

Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
We obtain broad sufficient conditions for reconstructing the coefficients of a Kolmogorov operator by means of a solution to the Cauchy problem for the corresponding Fokker–Planck–Kolmogorov equation.
Bogachev, V. I., Shaposhnikov, S. V.
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A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient

Numerical Mathematics: Theory, Methods and Applications, 2013
In this paper, a new discontinuous Galerkin method is developed for the parabolic equation with jump coefficients satisfying the continuous flow condition. Theoretical analysis shows that this method is $L^2$ stable. When the finite element space consists of interpolative polynomials of degrees $k$, the convergent rate of the semi-discrete ...
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Quasilinear equations with discontinuous coefficients.

2005
The main aim of this paper is to establish an a priori bound of \(\|u\|_{L^\infty (\Omega)}\) for the weak solutions \(u\in W^{1,q} (\Omega)\), \(q>n\) of the equation \(Lu=0\) almost everywhere in \(\Omega\), where \[ L\equiv\sum^N_{i,j=1}\frac {\partial}{\partial x_i}\left(a_{ij}(x,u)\frac{\partial u}{\partial x_j}\right)+ b(x,u)\tag{1} \] and ...
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Degenerated nonlinear hyperbolic equation with discontinuous coefficients

Proceedings of the Indian Academy of Sciences - Section A, 1985
The author considers a general nonlinear hyperbolic equation in the region \(Q:=D\times [0,T]\) where D is a bounded domain in \({\mathbb{R}}^ n\) with smooth boundary \(\Gamma\). It is assumed that D is partitioned by a hypersurface \(\Gamma_ 1\) into regions \(D_ 1\) and \(D_ 2\) and the notation \(\gamma =\Gamma_ 1\times [0,T]\), \(S=\Gamma \times ...
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Hyperbolic Systems with Discontinuous Coefficients: Examples

1988
Consider the initial value problem for a linear hyperbolic (n×n)-system in two variables $$\begin{array}{*{20}l}(\partial_{t}\ +\ \Lambda(x, t)\partial_{X})V\ =\ F(x,t)V\ +\ G(x,t),(x,t) \in IR^2\\V(x,0)\ =\ A(X), x\ \in\ IR\end{array}$$ (1) where Λ and F are (n×n)-matrices, Λ real valued and diagonal, and V, G, A are n-vectors.
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Stationary diffusion processes with discontinuous drift coefficients

St. Petersburg Mathematical Journal, 2013
Summary: The paper is devoted to the stationary Fokker-Planck equation \(\Delta u-\mathrm{div} (uf)=0\) with a locally bounded measurable vector field \(f\) defined on the entire \(\mathbb R^n\). The existence of a positive (not necessarily integrable) solution is proved.
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