scholarly journals Boundary value problem with shift for loaded hyperbolic-parabolic type equation involving fractional diffusion operator

2018 ◽  
Vol 28 (1) ◽  
pp. 82-90
Author(s):  
K.U. Khubiev ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Type Equation ◽  
Parabolic Type ◽  
Fractional Diffusion ◽  
Diffusion Operator ◽  
Parabolic Type Equation

scholarly journals NEW L1-GRADIENT TYPE ESTIMATES OF SOLUTIONS TO ONE-DIMENSIONAL QUASILINEAR PARABOLIC SYSTEMS

2010 ◽  
Vol 12 (01) ◽  
pp. 85-106 ◽  
Author(s):  
S. N. ANTONTSEV ◽  
J. I. DÍAZ
Keyword(s):  
Type Equation ◽  
Parabolic Type ◽  
Parabolic Systems ◽  
Diffusion Term ◽  
One Dimensional ◽  
First Order ◽  
Estimates Of Solutions ◽  
Gradient Type ◽  
Degenerate Type ◽  
Parabolic Type Equation

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton–Jacobi or conservation laws type.

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