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Determination of a diffusion coefficient in a quasilinear parabolic equation

100%

Kanca F.

Open Mathematics

2017

tom 15

nr 1

77-91

This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.

Deforming metrics of foliations

72%

Rovenski V., Wolak R.

Open Mathematics

2013

tom 11

nr 6

1039-1055

Let M be a Riemannian manifold equipped with two complementary orthogonal distributions D and D ⊥. We introduce the conformal flow of the metric restricted to D with the speed proportional to the divergence of the mean curvature vector H, and study the question: When the metrics converge to one for which D enjoys a given geometric property, e.g., is harmonic, or totally geodesic? Our main observation is that this flow is equivalent to the heat flow of the 1-form dual to H, provided the initial 1-form is D ⊥-closed. Assuming that D ⊥ is integrable with compact and orientable leaves, we use known long-time existence results for the heat flow to show that our flow has a solution converging to a metric for which H = 0; actually, under some topological assumptions we can prescribe the mean curvature H.

Ograniczanie wyników

2 Open Mathematics

1 Kanca F.

1 Rovenski V.

1 Wolak R.

1 2017

1 2013

Wyniki wyszukiwania

Determination of a diffusion coefficient in a quasilinear parabolic equation

Deforming metrics of foliations