Global existence and large time behavior of solutions to reaction-diffusion systems with large diffusion coefficients /
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Subjects: | |
| Online Access: | Link to OAKTrust copy ProQuest, Abstract |
| Abstract: | Systems of semilinear parabolic partial differential equations arise naturally in the modeling of certain reaction-diffusion processes. We consider m com ponent systems of the form ut = D A u + f( u ) on (r, T) x fl w ith continuous nonnegative initial d ata and homogenous Neumann boundary conditions. Here D is an m x m diagonal m atrix with positive entries on the main diagonal, f! is a sm ooth bounded domain in R n and / : R m --» R m is continuously differentiable. We show that if an a priori L1 estim ate which is independent of the diffusion coefficients and truncation is available for u and if the diffusion coefficients are sufficiently large, then the solution u exists for all time, is uniformly bounded and decays exponentially to its spatial average in L°°(fl). This work extends earlier work of Conway, Hoff and Smoller and, in addition, provides a global existence result with relatively weak assum ptions on the vector field /. |
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| Item Description: | "Major subject: Mathematics." Vita. |
| Physical Description: | vi, 63 leaves ; 28 cm |
| Bibliography: | Includes bibliographical references. |