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(Research report / Forskningsrapport, 2004)
We show existence of a unique, regular global solution of the parabolic-elliptic system
$u_t +f(t,x,u)_x+g(t,x,u)+P_x=(a(t,x) u_x)_x$
and $-P_{xx}+P=h(t,x,u,u_x)+k(t,x,u)$ with initial data
$u|_{t=0} = u_0$. Here ...
(Research report / Forskningsrapport, 2004)
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa--Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous ...
(Research report / Forskningsrapport, 2004)
The existence of a positive solution in a weighted Sobolev space for an homogeneous semilinear elliptic integro-differential Dirichlet problem is proved. The integral operator of the equation depends on a nonlinear function ...
(Research report / Forskningsrapport, 2004)
In this paper we study the solitary waves for the coupled system of Schrödinger-Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed ...