scholarly journals Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations

2005 ◽  
Vol 51 (3) ◽  
pp. 279-332 ◽  
Author(s):  
Marco Fuhrman ◽  
Gianmario Tessitore
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Parabolic Equations ◽  
Mild Solutions ◽  
Backward Stochastic Differential Equations ◽  
Semilinear Parabolic Equations ◽  
Semilinear Parabolic

scholarly journals Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in Lp

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Albert N. Sandjo ◽  
Célestin Wafo Soh
Keyword(s):  
Thin Film ◽  
Epitaxial Growth ◽  
Parabolic Equations ◽  
Mild Solutions ◽  
Film Theory ◽  
Well Posedness ◽  
Semilinear Parabolic Equations ◽  
Unified Framework ◽  
Time Estimates ◽  
Semilinear Parabolic

AbstractWe establish the well-posedness of boundary value problems for a family of nonlinear higherorder parabolic equations which comprises some models of epitaxial growth and thin film theory. In order to achieve this result, we provide a unified framework for constructing local mild solutions in C

On mild solutions of gradient systems in Hilbert spaces

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Andrzej Rozkosz
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Representation ◽  
Infinite Dimensional ◽  
The Cauchy Problem

AbstractWe consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

BACKWARD SDEs AND SOBOLEV SOLUTIONS FOR SEMILINEAR PARABOLIC PDEs WITH SINGULAR COEFFICIENTS

2011 ◽  
Vol 14 (03) ◽  
pp. 517-536 ◽  
Author(s):  
TUSHENG ZHANG ◽  
QIKANG RAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Parabolic Pdes ◽  
Singular Coefficients ◽  
Semilinear Parabolic ◽  
Backward Sdes

In this paper, we construct the solutions of semilinear parabolic PDEs with singular coefficients and establish the link to solutions of backward stochastic differential equations.

Sign in / Sign up

Export Citation Format

Share Document