Results 11 to 20 of about 1,893 (36)

Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation

, 2015
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous diffusion with ...
Carrillo, Jose Antonio, Vazquez, Juan Luis   +1 more
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Nonconcentration of energy for a semilinear Skyrme model

, 2010
We continue our investigation of a model introduced by Adkins and Nappi, in which omega mesons stabilize chiral solitons. The aim of this article is to show that the energy associated to equivariant solutions does not concentrate.Comment: 12 pages, 2 ...
Adkins, Balachandran, Balachandran, Christodoulou, Dan-Andrei Geba, Geba, Gladwell, Glimm, Grillakis, Grillakis, Lee, Rajeev, S.G. Rajeev, Shatah, Shatah, Skyrme, Turok, Witten, Witten   +18 more
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Some general new Einstein Walker manifolds

, 2012
In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manifold.
Jafari, Mehdi, Nadjafikhah, Mehdi
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Data Assimilation algorithm for 3D B\'enard convection in porous media employing only temperature measurements

, 2015
In this paper we propose a continuous data assimilation (downscaling) algorithm for the B\'enard convection in porous media using only coarse mesh measurements of the temperature.
Farhat, Aseel, Lunasin, Evelyn, Titi, Edriss S.   +2 more
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Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

, 2009
Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type $$ u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, $
Bakirova M I, Bebernes J, Bricmont J, Dalmasso R, Dold J W, Egorov Yu V, Fefferman C, Frank-Kamenetskii D A, Frank-Kamenetskii D A, Galaktinov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Guo Y, Hamilton R, Herrero M A, Herrero M A, Ibragimov N H, Joulin G Mikishev A B Sivashinsky G I, Kato T, Kurdyumov S P, Kurdyumov S P, Lepin L A, Lepin L A, Leray J, Levitan B M, Loewner C, Lunardi A, Maz'ja V, Mitidieri E, Naimark M A, Nussair E S, Ovsiannikov L V, Pao C V, Peletier L A, Quittner P, Samarskii A A, Semenov N, Svirshchevskii S R, Svirshchevskii S R, Tao T, V A Galaktionov, Velazquez J J L, Zel'dovich Ya B   +52 more
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Exact determination of the volume of an inclusion in a body having constant shear modulus

, 2014
We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus.
Milton, Graeme W., Thaler, Andrew E.
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Inviscid models generalizing the 2D Euler and the surface quasi-geostrophic equations

, 2010
Any classical solution of the 2D incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time.
Chae, Dongho, Constantin, Peter, Wu, Jiahong   +2 more
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Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions

, 2007
In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions.
A I Zenchuk, Ablowitz M J, Bogdanov L V, Bruschi M, Calogero F, Konopelchenko B, Korteweg D J, P M Santini, Santini P M Zenchuk A I, Tsarev S P, Whitham J B, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zenchuk A, Zenchuk A I, Zenchuk A I, Zenchuk A I   +20 more
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Sliding mode control for a phase field system related to tumor growth

, 2017
In the present contribution we study the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a viscous Cahn-Hilliard type equation for the phase variable with a reaction-diffusion equation for the nutrient.
Colli, Pierluigi, Gilardi, Gianni, Marinoschi, Gabriela, Rocca, Elisabetta   +3 more
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Infinitesimal symmetry transformations of matrix-valued differential equations: An algebraic approach

, 2018
The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations, they present ...
Papachristou, C. J.
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