Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$
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We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike ...
In this paper, we consider nonlinear Schrodinger equations of the following type: -Delta u(x) + V (x) u(x) -q(x)|u(x)|sigma u(x) =lambda u(x), x is an element of R-N, u is an element of H-1(R-N) \ {0}, where N >= 2 and sigma > 0. We concentrate on situatio ...
Royal Society of Edinburgh Scotland Foundation, Cambridge2013
Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...
We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511-547, 1989) proved that, when the damping term is bounded in space and time, the equation is well posed i ...
Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...
An effective method based on the regularization technique to solve the problem of the high-frequency electromagnetic field coupling to an overhead transmission line is presented. The integral-differential equation describing the field-induced current into ...
In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a m ...
We develop an effective distributed strategy for seeking the Pareto solution of an aggregate cost consisting of regularized risks. The focus is on stochastic optimization problems where each risk function is expressed as the expectation of some loss functi ...
In this paper we consider the equation for equivariant wave maps from R3+1 to S-3 and we prove global in forward time existence of certain C-infinity-smooth solutions which have infinite critical Sobolev norm (H) overdot(3/4) (R-3) x (H) overdot(1/2) (R-3) ...