The aim of this paper is to extend the usual framework of SPDE with monotone coefficients to include a large class of cases with merely locally monotone coefficients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic rea...

In this paper we derive the evolution equation of first nonzero eigenvalue (p,q)-Laplace system under unnormalized Hk-flow. By imposing some conditions on mean curvature prove monotonicity

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Ly...

3 4 CONTENTS Preface These lecture notes are intented as an introduction to linear second order elliptic partial differential equations. It can be considered as a continuation of a chapter on elliptic equations of the lecture notes [17] on partial differential equations. In [17] we focused our attention mainly on explicit solutions for standard problems for elliptic, parabolic and hyperbolic eq...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

Pseudo-Laplace transform is an important notion from pseudo-analysis’ framework that is often used in dealing with differential or integral equation. The (⊕, ̄)-Laplace transform considered here is a generalization of the pseudo-Laplace transform based on a special class of generalized pseudo-operations that need not be commutative nor associative. This pseudo-Laplace type transform has been use...