The final value theorem As with the initial value theorem, for a function f(t) having a Laplace transform F(s) we can write (equations [18] and [19]): [21]L{ddtf(t)}=∫0∞e−stddtf(t)dt=−f(0)+sF(s)As s tends to zero then e–st tends to 1 and so: lims→0[∫0...
This final report summarizes work accomplished on the development of marching algorithms for the numerical computation of ill-posed initial value problems. Applications include nonlinear inverse heat transfer in gun barrels, and the detection of flaws in metallic plates by ultrasonic testing. A new ...
This article is concerned with the existence of mild solutions to the initial value problem for a class of semilinear evolution equations with fractional order. New existence theorems are obtained by means of fixed point theorem for condensing maps. The
(16) and (17) can be obtained from a variational principle formulated as a boundary value problem in time. However for a causal description as an initial value problem, we must be able to determine the dynamics of the particle without knowledge of the final point of the trajectory. If one...
Before we formulate exact conditions on regular solution of the problems (1.1) and (1.2), expressed only by its operator coefficients, we must estimate the norms of inter- mediate derivative operators participating in the perturbed part of the given equation. Theorem the space 1 leads to the ...
Local existence of such a solution was proved in [23] (the first three steps in the proof of Theorem 6) for a little more general problems which contain Problem (1) as a special case, by applying Galerkin’s method and the contraction mapping principle. The lengthy proof will not be ...
Theorem 2.3Suppose thatf(z)satisfies(H), u_{0} \in H^{s+1}, andu_{1}\in H^{s+1}for somes>\frac{n}{2}+1, n\geq 1, then problem (1.1)–(1.2) has a unique local solutionu(x,t)defined on a maximal time interval[0,T_{0}), T_{0}>0, with...
aThe initial blank reading with the FRAP reagent alone was subtracted from the final reading of the FRAP reagent with the sample to determine the FRAP value of the sample. 最初的空白的读书与单独拉紧试剂从拉紧试剂的最后的读书被减去以样品确定样品的拉紧价值。 [translate] ...
As a result, this signifies the necessity of the development in numerical techniques for solving the problems to understand the nature of solution behaviors. Dutykh et al. solved the BBM-KdV equation using the traditional finite volume approach as well as explicit and implicit-explicit Runge–...
We opt to accept the second law at face value and assume that it describes a fundamental aspect of reality: time asymmetric boundary conditions (i.e., low initial entropy, high final entropy). Time-asymmetric boundary conditions are acceptable under the current understanding (or lack thereof) ...