Results 21 to 30 of about 191 (131)
Local existence result of the single dopant diffusion including cluster reactions of high order
Abstract and Applied Analysis, Volume 6, Issue 1, Page 13-34, 2001., 2001 We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction‐drift‐diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic ...
R. Bader, W. Merz
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Convergence of a finite volume scheme for a parabolic system applied to image processing
Moroccan Journal of Pure and Applied Analysis, 2022 We analyze a finite volume scheme for a nonlinear reaction-diffusion system applied to image processing. First, we demonstrate the existence of a solution to the finite volume scheme.
Attmani Jamal +2 more
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Attractors of multivalued semiflows generated by differential inclusions and their approximations
Abstract and Applied Analysis, Volume 5, Issue 1, Page 33-46, 2000., 2000 We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Alexei V. Kapustian, José Valero
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Asymptotic stability of an epidemiological fractional reaction-diffusion model
Demonstratio Mathematica, 2023 The aim of this article is to study the known susceptible-infectious (SI) epidemic model using fractional order reaction-diffusion fractional partial differential equations [FPDEs] in order to better describe the dynamics of a reaction-diffusion SI with ...
Djebara Lamia +2 more
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Reaction diffusion equations and quadratic convergence
International Journal of Stochastic Analysis, Volume 10, Issue 2, Page 179-186, 1997., 1996 In this paper, the method of generalized quasilinearization has been extended to reaction diffusion equations. The extension includes earlier known results as special cases. The earlier results developed are when (i) the right‐hand side function is the sum of a convex and concave function, and (ii) the right‐hand function can be made convex by adding a
A. S. Vatsala +2 more
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Flow invariance for perturbed nonlinear evolution equations
Abstract and Applied Analysis, Volume 1, Issue 4, Page 417-433, 1996., 2000 Let X be a real Banach space, J = [0, a] ⊂ R, A : D(A) ⊂ X → 2X\ϕ an m‐accretive operator and f : J × X → X continuous. In this paper we obtain necessary and sufficient conditions for weak positive invariance (also called viability) of closed sets K ⊂ X for the evolution system u′ + Au∍f(t, u) on J = [0, a].
Dieter Bothe
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On a comparison theorem for parabolic equations with nonlinear boundary conditions
Advances in Nonlinear Analysis, 2022 In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary ...
Kita Kosuke, Ôtani Mitsuharu
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Explicit solutions of Fisher′s equation with three zeros
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 617-620, 1990., 1990 Explicit traveling wave solutions of Fisher′s equation with three simple zeros ut = uxx + u(1 − u)(u − a), a ∈ (0, 1), are obtained for the wave speeds suggested by pure analytic considerations. Two types of solutions are obtained: one type is of a permanent wave form whereas the other is not.
M. F. K. Abur-Robb
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On the existence of the solution of Burgers′ equation for n ≤ 4
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 645-650, 1990., 1990 In this paper a proof of the existence of the solution of Burgers′ equation for n ≤ 4 is presented. The technique used is shown to be valid for equations with more general types of nonlinearities than is present in Burgers′ equation.
Adel N. Boules
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On the solution of reaction‐diffusion equations with double diffusivity
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 1, Page 163-172, 1987., 1986 In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more ...
B. D. Aggarwala, C. Nasim
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