Abstract The main goal of this paper is to obtain error bounds for parabolic integro-differential equation. derivation these based elliptic and Ritz -Volterra reconstructions introduced by Makridakis Nochetto 2003 then extended - Volterra reconstruction in case integro-parabolic differential problems Reddy Sinha 2015. We proved optimal order certain classes semilinear intergro equations. key po...

We consider three types of semilinear second order PDEs on a cylindrical domain Ω × (0,∞), where Ω is a bounded domain in N , N 2. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × (0,∞) is reserved for time t, the third type is an elliptic equation with a singled out unbounded variable t. We discuss the asymptotic behavior, as t ...

Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connec...

The blow-up rate estimate for the solution to a semilinear parabolic equation ut = ∆u+V (x)|u|p−1u in Ω×(0, T ) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x, 0) = Mφ(x) as M goes to infinity, which have been found in [5], are improved under some reason...

Abstract. For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large class of these equations, we show that some of the solutions which do not blow up actually tend to equilibria. The characterizing property of such solutions is a finite energy constraint, which comes about from the fact that this class of equations can be ...

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is eleme...

We study the large time behavior of positive solutions of the semilinear parabolic equation ut Uxx + e(g(u))x + f(u), 0 < x < L, e E R, subject to u(O,t) u(i,t) 0. The model problem in which the results apply is g(u) u and f(u) up 1 < m < p. The steady state problem is analyzed in some detail, and results about finite time blow up are proved.

The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem in all of the space is analyzed together with continuous dependence and a priori estimates of the solution. These estimates show that the asymptotic behavior ...

The inverse problem of identifying an unknown source control parameter in a semilinear parabolic equation under an integral overdetermination condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and finding the unknown parameter is derived. Finally, two ...

We consider a semilinear parabolic equation in a rectangular domain Ω ⊂ R: (∂tu)(x, t) = ∆u(x, t) + a(u(x, t)) with the zero initial value and suitable Dirichlet data. We discuss an inverse problem of determining the nonlinear term a(·) from Neumann data ∂u ∂n on ∂Ω × (0, T ). Under appropriate Dirichlet data, we prove conditional stability of the Hölder type in this inverse problem within a su...