On the Growth of Solutions of Quasi Liner Parabolic Equations
On the Growth of Solutions of Quasi Liner Parabolic Equations
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Thus, v satisfies 1^ - L[v] > -5v + Ne"^^ + p V + C |Vv | o t — o > -5v + a(x, t) + YANe"^* + P^v + C jVv 1 > (Y+p^-5)v + a(x, t) + clVv| > P(x, t, v, Vv), We again complete our proof by applying Theorem 1.
The only thing even slightly remarkable about Theorems 6 and 7 is the local nature of the assumptions on P j it should be emphasized, however, that our results merely assert that if a solution exists with smell boundary values, its (?rowth is determined. Nothing is said about whether such a ...solution exists, or how the gradient of a solution must behave, 6. Finite Escape Times We return here to a question raised in Section i;: When do solutions u(x, t) of (1), which satisfy given boundary conditions become infinite as t --> T^, where T^ is some finite number?
k^ To answer this, we must be able to bound ^'^^ u(x, t) fr( below; this we do in the following theorem.
THEOREM 8, We suppose that O is b ounde d, and t hat 2 1 u(x, t)CI C » in Qm, and satisf ies there ^ - Lfu] > G(u, t) (15) n where L = ) ^r^ (a.
What to read after On the Growth of Solutions of Quasi Liner Parabolic Equations?
You can find similar books in the "Read Also" column, or choose other free books by Stanley Kaplan to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Thus, v satisfies 1^ - L[v] > -5v + Ne"^^ + p V + C |Vv | o t — o > -5v + a(x, t) + YANe"^* + P^v + C jVv 1 > (Y+p^-5)v + a(x, t) + clVv| > P(x, t, v, Vv), We again complete our proof by applying Theorem 1.
The only thing even slightly remarkable about Theorems 6 and 7 is the local nature of the assumptions on P j it should be emphasized, however, that our results merely assert that if a solution exists with smell boundary values, its (?rowth is determined. Nothing is said about whether such a ...solution exists, or how the gradient of a solution must behave, 6. Finite Escape Times We return here to a question raised in Section i;: When do solutions u(x, t) of (1), which satisfy given boundary conditions become infinite as t --> T^, where T^ is some finite number?
k^ To answer this, we must be able to bound ^'^^ u(x, t) fr( below; this we do in the following theorem.
THEOREM 8, We suppose that O is b ounde d, and t hat 2 1 u(x, t)CI C » in Qm, and satisf ies there ^ - Lfu] > G(u, t) (15) n where L = ) ^r^ (a.
What to read after On the Growth of Solutions of Quasi Liner Parabolic Equations?
You can find similar books in the "Read Also" column, or choose other free books by Stanley Kaplan to read onlineMoreLess
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