Related papers: Numerical verification of solutions for nonlinear …
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
This paper investigates the initial boundary value problem for a fractional pseudo-parabolic equation with singular potential. The global existence and blow-up of solutions to the initial boundary value problem are obtained at low initial…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
This paper presents a modified quasi-reversibility method for computing the exponentially unstable solution of a nonlocal terminal-boundary value parabolic problem with noisy data. Based on data measurements, we perturb the problem by the…
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…
This paper is concerned with the proof of existence and numerical approximation of large-data global-in-time Young measure solutions to initial-boundary-value problems for multidimensional nonlinear parabolic systems of forward-backward…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…
In this manuscript, we establish the existence and sharp geometric regularity estimates for bounded solutions of a class of quasilinear parabolic equations in non-divergence form with non-homogeneous degeneracy. The model equation in this…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…
In this paper, the authors propose a numerical method to compute the solution of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial condition is a nonnegative function with compact support. The problem is split in…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
This paper is concerned with the local and global properties of nonnegative solutions for semilinear heat equation $u_t-\Delta u=u^p+M|\nabla u|^q$ in $\Omega\times I\subset \R^N\times \R$, where $M>0$, and $p,q>1$. We first establish the…
We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $\alpha\in (1,2)$. We study a spatial semidiscrete scheme with the…
This paper deals with the numerical methods for the reconstruction of source term in linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the…
In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular domains via semigroup theory and computer-assisted proofs.…
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances of gradient flows with general costs, including the…