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Displaying 581 –
600 of
1048
The soil water movement model
governed by the initial-boundary value problem for a quasilinear
1-D parabolic equation with nonlinear coefficients is considered.
The generalized statement of the problem is formulated. The
solvability of the problem is proved in a certain class of
functional spaces. The data assimilation problem for this model is
analysed. The numerical results are presented.
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with polyconvex energy) due to a forming cavity.
We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.
We consider the pseudo--laplacian, an anisotropic version of the -laplacian operator for . We study relevant properties of its first eigenfunction for finite and the limit problem as .
We consider the pseudo-p-Laplacian, an anisotropic
version of the p-Laplacian operator for . We study
relevant properties of its first eigenfunction for finite p and
the limit problem as p → ∞.
We consider the equations of isentropic gas dynamics in Lagrangian coordinates. We are interested in global interactions of large waves, and their relation to global solvability and well-posedness for large data. One of the main difficulties in this program is the possible occurrence of a vacuum, in which the specific volume is infinite. In this paper we show that the vacuum cannot be generated in finite time. More precisely, if the vacuum is present for some positive time, then it must be present...
We consider the solution operator to the -operator restricted to forms with coefficients in . Here denotes -forms with coefficients in , is the corresponding -space and is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula to . This solution operator will have the property . As an application of the solution formula we will be able to characterize compactness of the solution operator in terms of compactness of commutators...
In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.
We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter . The high-frequency (or: semi-classical) parameter is . We let and go to zero simultaneously. We assume that the zero energy is non-trapping for the underlying classical flow. We also assume that the classical trajectories starting from the origin satisfy a transversality condition, a generic assumption.Under these assumptions, we prove that the solution radiates in the outgoing...
We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data
for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier
integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic
manifold. The underlying canonical relation is associated to a ``sojourn time'' or
``Busemann function'' for geodesics. As a consequence we obtain some information about
the high frequency behavior of the scattering...
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