Special two-derivative Runge–Kutta pairs with extended stability regions for handling linear inhomogeneous systems

Existence and iterative schemes of an infinite system of two-variable functional Fredholm-type Riemann–Liouville fractional integral equations

Homogenization of Nonlinear Dissipative Wave Equations with Multiscale Temporal Oscillations

We develop a homogenization theory for nonlinear hyperbolic equations with rapid oscillations in space and multiple microscopic time scales. The model features a semilinear wave equation with oscillatory coefficients and separated nonlinearities: an amplitude-dependent potential and a gradient-dependent forcing term. U...

Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler–Riesz Equations with Large Initial Data of Spherical Symmetry

The compressible Euler–Riesz equations are fundamental with wide applications in astrophysics, plasma physics, and mathematical biology. In this paper, we are concerned with the global existence and nonlinear stability of finite-energy solutions of the multidimensional Euler–Riesz equations with large initial data of s...

Lack of uniform continuity of the flow map of a quadratic derivative nonlinear Schrödinger equation

Fractional optimal control problems with trajectory-dependent singular coefficients

We investigate a class of fractional optimal control problems governed by semilinear fractional differential equations with trajectory-dependent singular coefficients. The state equation is formulated using the Caputo fractional derivative and contains a singular coefficient of the form (t−s(t))−β\documentclass[12pt]{m...

The Dirichlet-to-Neumann Operator and a Nonlinear Boundary Value Problem on the Disk: A Complete Fourier-Analytic Solution