In this paper, we are interested in the problem of determining source function for Sobolev equation with fractional Laplacian. This is ill-posed sense Hadamard. order to edit instability solution, applied Landweber method. theoretical analysis results, show error estimate between exact solution and regularized by using an a priori regularization parameter choice rule posteriori rule. Finally, i...

The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence of the spectral formula chi(G)=sum_x (-1)^dim(x) = p(G)-n(G), where p(G) is the number of positive eigenvalues and n(G) is the number of negati...

A non linear Itô equation in a Hilbert space is studied by means of Girsanov theorem. We consider a non linearity of polynomial growth in suitable norms, including that of quadratic type which appears in the Kuramoto–Sivashinsky equation and in the Navier– Stokes equation. We prove that Girsanov theorem holds for the 1-dimensional stochastic Kuramoto–Sivashinsky equation and for a modification ...