Analyticity of solutions to fully nonlinear parabolic evolution equations on symmetric spaces

2004 ◽  
pp. 549-576
Author(s):  
Joachim Escher ◽  
Gieri Simonett
Keyword(s):  
Symmetric Spaces ◽  
Evolution Equations ◽  
Fully Nonlinear ◽  
Nonlinear Parabolic ◽  
Parabolic Evolution Equations

scholarly journals On a discrete scheme for time fractional fully nonlinear evolution equations

2020 ◽  
Vol 120 (1-2) ◽  
pp. 151-162 ◽  
Author(s):  
Yoshikazu Giga ◽  
Qing Liu ◽  
Hiroyoshi Mitake
Keyword(s):  
Fractional Derivatives ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Parabolic Pdes ◽  
Fully Nonlinear ◽  
Discrete Scheme ◽  
Nonlinear Parabolic Pdes ◽  
Nonlinear Parabolic ◽  
Convergence Of The Scheme

We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo’s time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can be viewed as a resolvent-type approximation.

scholarly journals Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials

2020 ◽  
pp. 1-31
Author(s):  
Bogdan–Vasile Matioc ◽  
Georg Prokert
Keyword(s):  
Stokes Flow ◽  
Evolution Equations ◽  
Single Layer ◽  
Two Phase ◽  
Layer Potential ◽  
Two Fluids ◽  
Flat Interface ◽  
Nonlinear Parabolic ◽  
Parabolic Evolution Equations ◽  
2D Space

We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.

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