Related papers: Diffusing non-local inflation: Solving the field e…
We propose one way to regularize the fluctuations generated during inflation, whose infrared (IR) corrections diverge logarithmically. In the case of a single field inflation model, recently, we proposed one solution to the IR divergence…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary $e$-folds. Solving the resulting partial…
We consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable $t$, the fractional order of the self-adjoint positive definite unbounded operator in a Hilbert space and a singular…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
In this paper we consider a one-dimensional diffusion equation on the interval $[0,1]$ satisfying non-Feller boundary conditions. As a consequence, the initial value Cauchy problem fails to preserve nonnegativity or boundedness.…
The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…
Classification theory on the existence and non-existence of local in time solutions for initial value problems of nonlinear heat equations are investigated. Without assuming a concrete growth rate on a nonlinear term, we reveal the…
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…
This paper investigates the initial value problem for a system of one-dimensional fourth-order dispersive partial differential-integral equations with nonlinearity involving derivatives up to second order. Examples of the system arise in…
We develop a non-linear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a non-perturbative manner, are invariant under changes of time slicing…
In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for diffusion-wave equation with the Caputo fractional derivative in a domain bounded by smooth curves. The uniqueness…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…
We show that the initial field values required to produce inflation in the two fields original hybrid model, and its supergravity F-term extension, do not suffer from any fine-tuning problem, even when the fields are restricted to be…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
This is a study of a class of nonlocal nonlinear diffusion equations. We present a strong maximum principle for nonlocal time-dependent Dirichlet problems. Results are for bounded functions of space, rather than (semi)-continuous functions.…
In this article, we study the long-time asymptotic properties of a non-linear and non-local equation of diffusive type which describes the rock-paper-scissors game in an interconnected population.We fully characterize the self-similar…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations…
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…