TY - JOUR
T1 - Stability of solutions of quasilinear parabolic equations
JF - J. Math. Anal. Appl. 308 (2005) 221-239
Y1 - 2005
A1 - Giuseppe Maria Coclite
A1 - Helge Holden
AB - We 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/2892
U1 - 1808
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Solitary waves for Maxwell Schrodinger equations
JF - Electron. J. Differential Equations (2004) 94
Y1 - 2004
A1 - Giuseppe Maria Coclite
A1 - Vladimir Georgiev
AB - In 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.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1582
U1 - 2536
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some results on the boundary control of systems of conservation laws
JF - SIAM J.Control Optim. 41 (2003),no.2, 607
Y1 - 2003
A1 - Alberto Bressan
A1 - Fabio Ancona
A1 - Giuseppe Maria Coclite
PB - SISSA Library
UR - http://hdl.handle.net/1963/1615
U1 - 2503
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -