This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space H

In this paper we study the Cauchy problem for the semilinear stochastic wave equation (@ 2

We solve the Cauchy problem of the Ward equation with both continuous and discrete scattering data.

Galerkin approximations to solutions of a Cauchy-Dirichlet problem governed by the generalized porous medium equation

We review different properties related to the Cauchy problem for the (nonlinear) Schrödinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadr...

We propose a discretized Tikhonov regularization for a Cauchy problem for an elliptic equation by a reproducing kernel Hilbert space. We prove the convergence of discretized regularized solutions to an exact solution. Our numerical results demonstrate that our method can stably reconstruct solutions to the Cauchy problems even in severe cases of geometric configurations.

We generalize the results of [22], [11], [8] to study the inverse scattering problem of the Ward equation with non-small data and solve the Cauchy problem of the Ward equation with a non-small purely continuous scattering data.

Symmetry is repetitive self-similarity. We proved the stability problem by replicating well-known Cauchy equation and Jensen into two variables. In this paper, we Hyers-Ulam of bi-additive functional f(x+y,z+w)=f(x,z)+f(y,w) bi-Jensen 4fx+y2,z+w2=f(x,z)+f(x,w)+f(y,z)+f(y,w).

The equation partial differential(t)u = u partial differential(xx)(2)u -(c-1)( partial differential(x)u)(2) is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self...

and Applied Analysis 3 The functional equation 1.7 was first solved by Kannappan. In fact he proved that a mapping f on a real vector space is a solution of 1.7 if and only if there exists a symmetric biadditive mapping B and an additive mapping A such that f x B x, x A x , for any x see 9 . The stability problem for 1.7 is also studied in 26 . Moreover 1.7 was pexiderized and solved by Kannapp...