Abstract. This paper is concerned with linear determinacy in monostable reactiondiffusion-convection equations and co-operative systems. We present sufficient conditions for minimal travelling-wave speeds (equivalent to spreading speeds) to equal values obtained from linearisations of the travelling-wave problem about the unstable equilibrium. These conditions involve both reaction and convection terms. We present separate conditions for non-increasing and non-decreasing travelling waves, called 'right' and 'left' conditions respectively, because of the asymmetry in propagation caused by the convection terms. We also give a necessary condition on the reaction term for the existence of convection terms such that both the right and left conditions can be satisfied simultaneously. Examples show that our sufficient conditions for linear determinacy are not necessary and compare these conditions in the scalar case with alternative conditions observed in Malaguti-Marcelli [15] and . We also illustrate, for both an equation and a system, the existence of reaction and (non-trivial) convection terms for which the right and left linear determinacy conditions are simultaneously satisfied. An example is given of an equation which is right but not left linearly determinate.
In this paper, fuzzy Aboodh transform used to solve system of fuzzy linear differential equations of first order in dimension two. Moreover, support work with an applied example in one of the institution.
In this article, a fuzzy Tarig evolve (T-n-transform) is implemented. Similar theorems and properties have been proven. To explain the technique of this fuzzy transform in differential equations, examples in real life are presented. This study shows the applicability of this interesting fuzzy transform for solving differential equations with constant coefficients also for its computational power. It is desirable to use it as a new technique, to not only solve “nonlinear fractional differential equations", and to analyze prelocal system information. Moreover, significant theorems are presented to explain the properties of T˜-transform as well as a suggested method is validated with two reality examples.
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