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Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

100%
Guliyev V. S., Omarova M. N.
Open Mathematics
|
2016
|
tom 14
|
nr 1
49-61
EN
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space [...] W˙2,1p,φ(Q,ω)$\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.
2
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Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

100%
Borsuk M., Wiśniewski D.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2051-2072
EN
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
3
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Global and exponential attractors for a Caginalp type phase-field problem

81%
Bangola B.
Open Mathematics
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2013
|
tom 11
|
nr 9
1651-1676
EN
We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
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