Criteria for Blow‐Up Phenomena for Solutions to Nonlinear Reaction–Diffusion Equations on Cones
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DOI: 10.1002/mma.70017
Abstract: This paper investigates the global and nonglobal existence of solutions to nonlinear reaction‐diffusion equations with a general nonlinearity and time‐dependent sources defined on cones of Euclidean spaces. More precisely, the purpose of this work is… read more here.
Keywords: solutions nonlinear; diffusion equations; nonlinear reaction; reaction diffusion ... See more keywords
Inverse source problem with a posteriori boundary measurement for fractional diffusion equations
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DOI: 10.1002/mma.9432
Abstract: In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class of… read more here.
Keywords: fractional diffusion; time; diffusion equations; inverse source ... See more keywords
An Adaptive Difference Method for Variable-Order Diffusion Equations
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DOI: 10.1007/s00009-024-02681-6
Abstract: An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional-time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of these timesteps is… read more here.
Keywords: variable order; method; diffusion equations; difference ... See more keywords
A numerical scheme to solve a class of two-dimensional nonlinear time-fractional diffusion equations of distributed order
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DOI: 10.1007/s00366-020-01185-7
Abstract: This article is devoted to obtain the numerical solution for a class of nonlinear two-dimensional distributed-order time-fractional diffusion equations. We discretize the problem by using a finite difference scheme in the time direction. Then, we solve… read more here.
Keywords: fractional diffusion; distributed order; time fractional; time ... See more keywords
The stability condition for the FDTD of the optical diffusion equations
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DOI: 10.1007/s10043-019-00567-7
Abstract: The finite-difference time-domain (FDTD) method, which is often used to solve Maxwell’s equations, has been proposed to solve the optical diffusion equations to simulate light propagation in turbid media such as biological tissue. Finite-difference methods… read more here.
Keywords: optical diffusion; condition; diffusion equations; stability condition ... See more keywords
Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations
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DOI: 10.1007/s10543-018-0697-x
Abstract: This paper focuses on the time–space fractional convection–diffusion equations with time fractional derivative (of order $$\alpha $$α, $$0< \alpha read more here.
Keywords: convection diffusion; space; time; diffusion equations ... See more keywords
Non-local Diffusion Equations Involving the Fractional $$p(\cdot )$$p(·)-Laplacian
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DOI: 10.1007/s10884-019-09745-2
Abstract: In this paper we study a class of nonlinear quasi-linear diffusion equations involving the fractional $$p(\cdot )$$p(·)-Laplacian with variable exponents, which is a fractional version of the nonhomogeneous $$p(\cdot )$$p(·)-Laplace operator. The paper is divided… read more here.
Keywords: involving fractional; cdot laplacian; fractional cdot; diffusion equations ... See more keywords
Localized and Expanding Entire Solutions of Reaction–Diffusion Equations
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DOI: 10.1007/s10884-020-09936-2
Abstract: This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction–diffusion equations in $$\mathbb {R}^N$$ R N in any space dimension N . The solutions are assumed to be localized… read more here.
Keywords: reaction diffusion; solutions reaction; entire solutions; diffusion equations ... See more keywords
Nonclassical Symmetries of a System of Nonlinear Reaction-Diffusion Equations
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DOI: 10.1007/s10958-019-04229-6
Abstract: We study the conditional symmetry of a system of nonlinear reaction-diffusion equations and establish the existence of operators of conditional symmetry for systems of nonlinear reaction-diffusion equations with any number of independent variables and find… read more here.
Keywords: diffusion equations; system nonlinear; nonlinear reaction; reaction diffusion ... See more keywords
Differential quadrature method for space-fractional diffusion equations on 2D irregular domains
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DOI: 10.1007/s11075-017-0464-0
Abstract: In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by Lévy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature… read more here.
Keywords: fractional diffusion; diffusion; space fractional; diffusion equations ... See more keywords
Finite difference and spectral collocation methods for the solution of semilinear time fractional convection-reaction-diffusion equations with time delay
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DOI: 10.1007/s12190-019-01267-w
Abstract: In this paper, an efficient numerical method is constructed to solve the nonlinear fractional convection-reaction-diffusion equations with time delay. Firstly, we discretize the time fractional derivative with a second order finite difference scheme. Then, Chebyshev… read more here.
Keywords: equations time; time; convection reaction; reaction diffusion ... See more keywords