Well-posedness of stochastic partial differential equations with Lyapunov condition

Stochastic Partial Differential Equations

Lyapunov inequalities for partial differential equations ✩

This paper is devoted to the study of Lp Lyapunov-type inequalities (1 p +∞) for linear partial differential equations. More precisely, we treat the case of Neumann boundary conditions on bounded and regular domains in RN . It is proved that the relation between the quantities p and N/2 plays a crucial role. This fact shows a deep difference with respect to the ordinary case. The linear study i...

Well-posedness of Boundary-value Problems for Partial Differential Equations of Even Order

In this article, we establish the well-posedness of two boundary value problems for 2k-th order partial differential equations. It is shown that the solvability of these problems depends on the evenness and oddness of the number k.

Well-posedness and asymptotics of some nonlinear integro-differential equations

We will prove the well-posedness of certain second order ordinary and partial integro-differential equations with an integral term of the form t ∫ 0 m(φ(t−s))φ̇(s) ds, wherem is given and φ is the solution. The new aspect is the dependence of the kernel on the solution. In addition, for the ordinary integro-differential equation, the asymptotic behaviour of the solution is described for some ker...

Well-posedness of parabolic differential and difference equations

The stable difference scheme for the approximate solution of the initial value problem ( ) ( ) ( ) ( ) 1 2 , t du t D u t Au t f t dt + + = ( ) 0 1, 0 0 t u < < = for the differential equation in a Banach space E with the strongly positive operator A and fractional operator 1 2 t D is presented. The well-posedness of the difference scheme in difference analogues of spaces of smooth functions is...