Search
Search Results
-
-
The Cable Equation
In Chapter 6, we studied a simple version of the cable equation, where a diffusion term was added to the FitzHugh-Nagumo equations. In this chapter,...
-
Problem with a Bitsadze–Samarskii Condition on Parallel Characteristics for a Mixed Type Equation of the Second Kind
AbstractFor a mixed type equation of the second kind, we prove the uniqueness and existence of a solution of the boundary value problem with the...
-
The Laplace Equation
In this chapter, the Laplace equation is introduced. They are given the basic properties of elliptic problems, the fundamental solutions, integral...
-
Time-averaging principle for G-SDEs based on Lyapunov condition
In this paper, we tame the uncertainty about the volatility in time-averaging principle for stochastic differential equations driven by G-Brownian...
-
Vallée-Poussin theorem for fractional functional differential equations with integral boundary condition
This research paper focuses on the study of a Riemann-Liouville fractional functional differential equation and a linear continuous operator acting...
-
Fixed Point Results for the Fractional Nonlinear Problem with Integral Boundary Condition
In this article, we study an integral boundary condition problem. In fact, we consider a new nonlinear fractional integro-differential equation with...
-
Non-local and Inverse Problems for the Rayleigh-Stokes Equation
This work consists of two parts. In the first part, a non-local boundary value problem is studied for the fractional version of the Rayleigh-Stokes...
-
The Heat Equation
This chapter deals with the heat equation. They are considered the weak and strong maximum principles, the Cauchy problem, the mean value formula,...
-
Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère Equation
We introduce two hybridizable discontinuous Galerkin (HDG) methods for numerically solving the two-dimensional Monge–Ampère equation. The first HDG...
-
Gellerstedt Problem with a Nonlocal Parity Boundary Condition
AbstractIn this work, for the Lavrentiev–Bitsadze equation, the problem Gellerstedt with a nonlocal boundary condition in the form of a parity...
-
Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients
We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in t and Lipschitz continuous in x . Combining a recent conditional...
-
Features of Numerical Reconstruction of a Boundary Condition in an Inverse Problem for a Reaction–Diffusion–Advection Equation with Data on the Position of a Reaction Front
AbstractA new approach to the reconstruction of a boundary condition in an inverse problem for a nonlinear singularly perturbed...
-
A Boundary Value Problem with a Conormal Derivative for a Mixed-Type Equation of the Second Kind with a Conjugation Condition of the Frankl Type
AbstractIn this paper, using the properties of generalized solutions in both the hyperbolic part and the elliptic part of a mixed domain, we study a...
-
On Correctness of a Mixed Problem for the Heat Equation with the Mixed Derivative in the Boundary Condition
AbstractWe consider an initial-boundary value problem for the heat equation with an inhomogeneous initial condition and boundary conditions. One of...
-
Strong-Norm Convergence of the Errors of the Projective-Difference Method with the Crank–Nicolson Scheme in Time for a Parabolic Equation with a Periodic Condition on the Solution
AbstractIn a separable Hilbert space, a smoothly solvable linear variational parabolic equation with a periodic condition on the solution is solved...
-
An Inverse Problem for a Quasilinear Elliptic Equation
We consider the inverse problem for a quasilinear second order elliptic equation with the unknown coefficient at the lower-order term and the first...
-
Solving A Nonlinear Equation
In this chapter, one of the more common mathematical problems is studied, which is to find the solution, or solutions, of an equation of the form...
-
Boundary Value Problems for a Parabolic-Hyperbolic Equation with Nonlinear Loaded Terms
AbstractIn the present work local and nonlocal boundary value problem involves nonlinear gluing condition for a loaded parabolic-hyperbolic type...
-
Condition numbers of Hessenberg companion matrices
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of...