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Optimal time and space regularity for solutions of degenerate differential equations

100%
Favaron A.
Open Mathematics
|
2009
|
tom 7
|
nr 2
249-271
EN
We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.
2
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The nonlinear diffusion equation of the ideal barotropic gas through a porous medium

100%
Zhan H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
895-906
EN
The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of the solutions may be obtained without any boundary condition.
3
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The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

84%
Pan J.
Open Mathematics
|
2011
|
tom 9
|
nr 3
673-685
EN
In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.
4
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Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations

84%
Li J., Yin J., Jin C.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1435-1447
EN
This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources.
5
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The area preserving curve shortening flow with Neumann free boundary conditions

84%
Mäder-Baumdicker E.
Geometric Flows
|
2015
|
tom 1
|
nr 1
EN
We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.
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