Partial defferential equations as inverse problem of moments

PINTARELLI, MARÍA B.; VERICAT, FERNANDO

Guanajuato

Congreso; Mathematical Congress of the Americas 2013 (MCA 2013); 2013

Centro de Investigaciones en Matemática (CIMAT) CONACYT - México

We consider specific cases of partial differential equations of first and second order linear and non-linear, for example the Klein-Gordon equation, the Poisson equation, and equations of the form a(x,t)w(x,t)+b(x,t)dw(x,t)/dt=h(x,t)w(x,t) If F(w(x,t))=0 is an equation in partial derivatives, then to find a solution to this equation, subject to boundary conditions in D is equivalent to solve a Fredholm integral equation of first kind, which in turn can be resolved as a problem of moments of bi-dimensional Hausdorff or as an inverse problem of generalized moments. We will find an approximated solution of F(w(x,t))=0 and bounds for the error of the estimated solution using the techniques on problem of moments. Each case is illustrated with examples.