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 作者：Piermarco Cannarsa , Wei Cheng 来源：[J].Calculus of Variations and Partial Differential Equations(IF 1.236), 2017, Vol.56 (5) 摘要：For autonomous Tonelli systems on $$\mathbb {R}^n$$ , we develop an intrinsic proof of the existence of generalized characteristics using sup-convolutions. This approach, together with convexity estimates for the fundamental solution, leads to new results such as the global propa...
 作者：Paolo Albano , Piermarco Cannarsa , Carlo Sinestrari 来源：[J].Journal of Differential Equations(IF 1.48), 2020, Vol.268 (4), pp.1412-1426 摘要：Abstract(#br)We study the generation of singularities from the initial datum for a solution of the Cauchy problem for a class of Hamilton-Jacobi equations of evolution. For such equations, we give conditions for the existence of singular generalized characteristics starting at th...
 作者：Piermarco Cannarsa , Qinbo Chen , Wei Cheng 来源：[J].Journal of Differential Equations(IF 1.48), 2019, Vol.267 (4), pp.2448-2470 摘要：Abstract(#br)For mechanical Hamiltonian systems on the torus, we study the dynamical properties of the generalized characteristic semiflows associated with the Hamilton-Jacobi equations, and build the relation between the ω -limit sets of the semiflows and the projected Aubr...
 作者：Piermarco Cannarsa , Giuseppe Floridia , Alexander Y. Khapalov 来源：[J].Journal de mathématiques pures et appliquées(IF 1.174), 2017 摘要：Abstract(#br)We study the global approximate controllability properties of a one-dimensional semilinear reaction–diffusion equation governed via the coefficient of the reaction term. It is assumed that both the initial and target states admit no more than finitely many chang...
 作者：Piermarco Cannarsa , Alexander Khapalov 来源：[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2018, Vol.465 (1), pp.100-124 摘要：Abstract(#br)We study the local controllability properties of generic 2- D and 3- D bio-mimetic swimmers employing the change of their geometric shape to propel themselves in an incompressible fluid described by the Navier–Stokes equations. It is assumed that swimmers' bodie...
 作者：Paolo Albano , Piermarco Cannarsa , Teresa Scarinci 来源：[J].Journal of Differential Equations(IF 1.48), 2018, Vol.264 (5), pp.3312-3335 摘要：Abstract(#br)In a bounded domain of R n with boundary given by a smooth ( n − 1 ) -dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields { X 1 , … , X N } subject to Hörmander's brac...
 作者：Vincenzo Basco , Piermarco Cannarsa , Hélène Frankowska 来源：[J].Nonlinear Analysis(IF 1.64), 2019, Vol.184, pp.298-320 摘要：Abstract(#br)Regularity properties are investigated for the value function of the Bolza optimal control problem with affine dynamic and end-point constraints. In the absence of singular geodesics, we prove the local semiconcavity of the sub-Riemannian distance from a compact...
 作者：Piermarco Cannarsa , Antonio Marigonda , Khai T. Nguyen 来源：[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2015, Vol.427 (1), pp.202-228 摘要：Abstract(#br)We study the time optimal control problem with a general target S for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the boundary of S . Consequently, the mi...
 作者：Piermarco Cannarsa , Fabio S. Priuli 来源：[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2015, Vol.429 (2), pp.1059-1085 摘要：Abstract(#br)We introduce and investigate the wellposedness of two models describing the self-propelled motion of a “small bio-mimetic swimmer” in the 2- D and 3- D incompressible fluids modeled by the Navier–Stokes equations. It is assumed that the swimmer's body consi...
 作者：Fabio Ancona , Piermarco Cannarsa , Khai T. Nguyen 来源：[J].Archive for Rational Mechanics and Analysis(IF 2.292), 2016, Vol.219 (2), pp.793-828 摘要：Abstract(#br) We study quantitative compactness estimates in $${\mathbf{W}^{1,1}_{{\rm loc}}}$$ for the map $${S_t}$$ , $${t > 0}$$ that is associated with the given initial data $${u_0\in {\rm Lip} (\mathbb{R}^N)}$$ for the corresponding solution $${S_t u_0}$$ of a Hamilton...