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Díaz Díaz, Jesús Ildefonso ; Bejenaru, Ioan ; Vrabie, Ioan I. | Texas State University, Department of Mathematics | 2001The authors obtain an approximate controllability result for the nonlinear equation $y'+Ay+F(t,y)y=h(t)$ with the initial condition where $x$ is the control and $A$ generates a $C_0$-semigroup in a Hilbert space. The Schauder fixed poi[...]texto impreso
We show some compactness properties of the operator f--u, where u is the solution of the nonlinear diffusion equation ut???(u)=f on (0,T)×? associated with the parabolic boundary conditions ?(u)=0 on (0,T)×?? and u(0,?)=u0(?) on ?, u0 a given fu[...]texto impreso
The authors study the existence of weak solutions for the following system: ut???(u)?F(u,v), vt???(v)?G(u,v) in (0,T)×?, ?(u)=?(v)=0 on (0,T)×??, u(0,x)=u0(x), v(0,x)=v0(x) in the region ???Rn with smooth boundary ??. The functions ?,?:R?R are a[...]
