We study fully nonlinear second-order(forward)stochastic PDEs.They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework.For the most general fully nonlinear cas...We study fully nonlinear second-order(forward)stochastic PDEs.They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework.For the most general fully nonlinear case,we develop a local theory of classical solutions and then define viscosity solutions through smooth test functions.Our notion of viscosity solutions is equivalent to the alternative using semi-jets.Next,we prove basic properties such as consistency,stability,and a partial comparison principle in the general setting.If the diffusion coefficient is semilinear(i.e,linear in the gradient of the solution and nonlinear in the solution;the drift can still be fully nonlinear),we establish a complete theory,including global existence and a comparison principle.展开更多
In a recent study in Nature,1 Shapira et al.reported that the peptidomimetic compound N-0385 inhibited SARS-CoV-2 infection in vitro in remarkably low concentrations by blocking the host cell protease TMPRSS2,which me...In a recent study in Nature,1 Shapira et al.reported that the peptidomimetic compound N-0385 inhibited SARS-CoV-2 infection in vitro in remarkably low concentrations by blocking the host cell protease TMPRSS2,which mediates proteolytic cleavage of the SARS-CoV-2 major surface glycoprotein spike(S).Accordingly,N-0385 protected experimentally infected mice from severe SARS-CoV-2 pathology.展开更多
文摘We study fully nonlinear second-order(forward)stochastic PDEs.They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework.For the most general fully nonlinear case,we develop a local theory of classical solutions and then define viscosity solutions through smooth test functions.Our notion of viscosity solutions is equivalent to the alternative using semi-jets.Next,we prove basic properties such as consistency,stability,and a partial comparison principle in the general setting.If the diffusion coefficient is semilinear(i.e,linear in the gradient of the solution and nonlinear in the solution;the drift can still be fully nonlinear),we establish a complete theory,including global existence and a comparison principle.
基金Open Access funding enabled and organized by Projekt DEAL.
文摘In a recent study in Nature,1 Shapira et al.reported that the peptidomimetic compound N-0385 inhibited SARS-CoV-2 infection in vitro in remarkably low concentrations by blocking the host cell protease TMPRSS2,which mediates proteolytic cleavage of the SARS-CoV-2 major surface glycoprotein spike(S).Accordingly,N-0385 protected experimentally infected mice from severe SARS-CoV-2 pathology.
