Electroosmotic and Hydrodynamic Oscillations in the Teorell Membrane System

Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations

In this paper we shall introduce new constructions of approximate solutions of general linear partial differential equations with constant coefficients on the whole spaces, and establish fundamental estimates of the solutions depending on the inhomogeneous terms. This will be done by combining general ideas of the Tikhonov regularization and discretization of bounded linear operator equations on reproducing kernel Hilbert spaces. Furthermore, we will provide approximate solutions for the related inverse source problems.

This paper presents the applicati on of a general purpose partial differential equation solver, called PDEase2D and the associated soil property functions to the analysis of saturated-unsaturated seepage problem. Examples of steady state and transient seepage through an earth dam are used to illustrate the use of PDEase2D in solving saturated-unsaturated seepage problems.

Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent?

The method of characteristics is applied in studying general quasilinear partial differential equations of first order sich as, for example, convection or transport equations. It is shown how the notion of characteristics allows for reducing the considerations to those for nonlinear systems of ordinary differential equations. An application to the continuity equation describing mass conservation completes this chapter.

The existence, uniqueness and some sufficient conditions for stability in distribution of mild solutions to stochastic partial differential delay equations with jumps are presented. The principle technique of our investigation is to construct a proper approximating strong solution system and carry out a limiting type of argument to pass on stability of strong solutions to mild ones. As a consequence, stability results of Basak et al . ( Basak et al . 1999 J. Math. Anal. Appl. 202 , 604–622) and Yuan et al . ( Yuan et al . 2003 Syst. Control Lett. 50 , 195–207) are generalized to cover a class of much more general stochastic partial differential delay equations with jumps in infinite dimensions. In contrast to the almost sure exponential stability in Ichikawa ( Ichikawa 1982 J. Math. Anal. Appl. 90 , 12–44) and Luo & Liu ( Luo & Liu 2008 Stoch. Proc. Appl. 118 , 864–895) and the moment exponential stability in Luo & Liu, we present a new result on the stability in distribution of mild solutions. Finally, an example is given to demonstrate the applicability of our work.

A very general partial differential equation in space and time satisfied by the gene frequency in a monoecious population distributed continuously over an arbitrary habitat is derived. The treatment is restricted to a single diallelic locus in the absence of mutation and random drift, and it is supposed that time is continuous, births and deaths occur at random, and migration is independent of genotype. With the further assumptions that migration is isotropic and homogeneous, the population density is constant and uniform (as permitted by the population regulation mechanism included in the formulation), and Hardy-Weinberg proportions obtain locally, this partial differential equation reduces to the simplest multidimensional generalization of the classical Fisher-Haldane cline model. The efficacy of migration and selection in maintaining genetic variability at equilibrium in this model is investigated by deducing conditions for the existence of clines under various circumstances. The effects of the degree of dominance, a neutral belt between the regions where a particular allele is advantageous and deleterious, finiteness of the habitat, and habitat dimensionality are evaluated. Provided at least one of the alleles is favored only in a finite region, excluding the special case in which its total effective selective coefficient is zero, if conditions for supporting a cline are too unfavorable because migration is too strong, selection is too weak, or both, a cline cannot exist at all. Thus, unless there is overdominance, the population must be monomorphic. It is possible for a cline which can barely exist under the prevailing ecological circumstances to show a large amount of variation in gene frequency.

In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the Laplacian to various forms of boundary integral equations based on the direct approach. This reduction can be easily extended to more general partial differential equations. Here we will consider, in particular, the Helmholtz equation, the Lame system, the Stokes equations and the biharmonic equation.

The primary aim is to develop a new class of pseudo-differential operators involving Linear Canonical Transform (LCT) and some of its essential results in Schwartz space and tempered distribution space. The secondary aim is to find applications of the LCT while constructing new general partial differential equations (Heat and Wave) and derive their solutions. Further, we have discussed particular cases of these partial differential equations. Furthermore, we have also shown the resolution of the solution of these equations graphically.

usual boundary conditions, and constraints u~U(t, z)~Em, where the control space U = U(t, z) is a given subset of Era. Here z =(z 1 . . . . . : ) are state variables and u =(u 1 .. . . , u m) control variables. As stated by P. K. RASHEVSKY [6], very general partial differential equations and systems can be written locally in the form (2). For instance, second order partial differential equations such as z~,+z~s= 1 u) can be immediately written in the form f ( t , s, z 1, zlt, z~,

In this paper, we introduce the operators related to mixed boundary value problems for general linear elliptic partial complex differential equations in the unit disc of the complex plane. The solvability of the relevant boundary value problems will be studied by transforming them into singular integral equations.

We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the feedback function using finitely based approximations. Using structural assumptions on the finitely based approximations, rates for the approximation error of the cost can be obtained. Our algorithm significantly reduces the computational complexity of finding controls with asymptotically optimal cost. Numerical experiments using artificial neural networks as well as radial basis function networks illustrate the performance of our algorithm. Our approach can also be applied to stochastic control problems for high dimensional stochastic differential equations and more general stochastic partial differential equations.

In this paper thermal conductivity analysis of insulating coating is discussed. The general partial differential thermal conductivity equation is used with consideration to nonlocal boundary effects. We relying on the Eringen’s approach involves heat-flow vector transformation using nonlocal influence function and weight coefficients. Also presented model includes own surface radiation of the coating.

Study of film boiling in He II by pressure and temperature oscillation measurements

Remarks on the Dirichlet problem for general linear partial differential equations