Related papers: Finite Time Blowup of Integer- and Fractional-Orde…
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of a logistic type reaction-diffusion equation. The finite time blowup results for nonnegative solutions under various restrictions on the coefficients…
This article is concerned with a semilinear time-fractional diffusion equation with a superlinear convex semilinear term in a bounded domain $\Omega$ with the homogeneous Dirichlet, Neumann, Robin boundary conditions and non-negative and…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions,…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
In this paper we consider the long time behavior of solutions of the initial value problem for the damped wave equation of the form \begin{eqnarray*} u_{tt}-\rho(x)^{-1}\Delta u+u_t+m^2u=f(u) \end{eqnarray*} with some $\rho(x)$ and $f(u)$…
We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow up of solutions subject to…
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…
In this paper we study a system of delay differential equations from the viewpoint of a finite time blow-up of the solution. We prove that the system admits a blow-up solution, no matter how small the length of the delay is. In the…
The aim of this paper is to refine some results concerning the blow-up of solutions of the exponential reaction-diffusion equation. We consider solutions that blow-up in finite time, but continue to exist as weak solutions beyond the…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
This article is concerned with semilinear time-fractional diffusion equations with polynomial nonlinearity $u^p$ in a bounded domain $\Omega$ with the homogeneous Neumann boundary condition and positive initial values. In the case of $p>1$,…
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically,…