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2e) is vacuous. 1. Thus, uniqueness holds over this broader class. We pass now to uniqueness for reaction-diffusion systems. 4. 11) is unique within the class V. 2. Then u, w E C([O, T o ] ; L"(R)), hence, have range in a bounded subset of R". Thus, there is no loss of generality in assuming that f is Lipschitz, since it is assumed C' and, hence, locally Lipschitz. 11). 1. Formulations for Parabolic Models 42 For a fixed i = 1 , . . 11) holds for all 0 < t c T o . 11) is summed on i, we obtain, for each 0 < t < T o , m 1 1 1 i= 1 c JO i 1 llui - W i l l t z ( n ) d z .

2e) is vacuous. 1. Thus, uniqueness holds over this broader class. We pass now to uniqueness for reaction-diffusion systems. 4. 11) is unique within the class V. 2. Then u, w E C([O, T o ] ; L"(R)), hence, have range in a bounded subset of R". Thus, there is no loss of generality in assuming that f is Lipschitz, since it is assumed C' and, hence, locally Lipschitz. 11). 1. Formulations for Parabolic Models 42 For a fixed i = 1 , . . 11) holds for all 0 < t c T o . 11) is summed on i, we obtain, for each 0 < t < T o , m 1 1 1 i= 1 c JO i 1 llui - W i l l t z ( n ) d z .

Andersland and D. M. ” McGraw-Hill, New York, 1978. D. M. Anderson and N. R. Morgenstern, Physics, chemistry and mechanics of frozen ground, in Proceedings, North American Permafrost Second International Conference, 2nd pp. , 1973. R. Aris, “The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts,” Vol. I. Oxford Univ. Press (Clarendon), London and New York, 1975. 44 [4] [5] [6] [7] [8] [9] [lo] [I I] [I21 [ 131 [I41 [ 151 [I61 [I71 [I81 [I91 [20] [21] [22] [23] [24] [25] 1. Formulations for Parabolic Models J.

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