01073nas a2200121 4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915 2007 en_Ud 00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/290701579nas a2200121 4500008004100000245007400041210006700115260001800182520117500200100001801375700002801393856003601421 2005 en d00aOn the attainable set for Temple class systems with boundary controls0 aattainable set for Temple class systems with boundary controls bSISSA Library3 aConsider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/158100982nas a2200121 4500008004100000245006900041210006900110260001800179520057400197100002800771700002500799856003600824 2005 en d00aConservation laws with time dependent discontinuous coefficients0 aConservation laws with time dependent discontinuous coefficients bSISSA Library3 aWe consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/166601445nas a2200121 4500008004300000245006200043210006200105260001300167520106100180100002801241700001801269856003601287 2005 en_Ud 00aStability of solutions of quasilinear parabolic equations0 aStability of solutions of quasilinear parabolic equations bElsevier3 aWe bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth.1 aCoclite, Giuseppe Maria1 aHolden, Helge uhttp://hdl.handle.net/1963/289201069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158400759nas a2200121 4500008004100000245005300041210005300094260001800147520038500165100002800550700002300578856003600601 2004 en d00aSolitary waves for Maxwell Schrodinger equations0 aSolitary waves for Maxwell Schrodinger equations bSISSA Library3 aIn this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated.1 aCoclite, Giuseppe Maria1 aGeorgiev, Vladimir uhttp://hdl.handle.net/1963/158200362nas a2200109 4500008004100000245005400041210005400095260001000149653002900159100002800188856003600216 2003 en d00aControl Problems for Systems of Conservation Laws0 aControl Problems for Systems of Conservation Laws bSISSA10aAsymptotic Stabilization1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/532500338nas a2200097 4500008004100000245006000041210005700101260001800158100002800176856003600204 2003 en d00aAn interior estimate for a nonlinear parabolic equation0 ainterior estimate for a nonlinear parabolic equation bSISSA Library1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/162200426nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700002800240856003600268 2003 en d00aSome results on the boundary control of systems of conservation laws0 aSome results on the boundary control of systems of conservation bSISSA Library1 aBressan, Alberto1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/161500716nas a2200121 4500008004300000245006000043210005300103260000900156520034400165100002100509700002800530856003600558 2002 en_Ud 00aOn the Boundary Control of Systems of Conservation Laws0 aBoundary Control of Systems of Conservation Laws bSIAM3 aThe paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.1 aBressan, Alberto1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/307000546nas a2200109 4500008004300000245008800043210006900131260001000200520016200210100002800372856003600400 2002 en_Ud 00aA multiplicity result for the Schrodinger-Maxwell equations with negative potential0 amultiplicity result for the SchrodingerMaxwell equations with ne bIMPAN3 aWe prove the existence of a sequence of radial solutions with negative energy of the SchrÃ¶dinger-Maxwell equations under the action of a negative potential.1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/3053