Local Analyticity in the Time and Space Variables and the Smoothing Effect for the Fifth-Order KdV-Type Equation
We consider the initial value problem for the reduced fifth-order KdV-type equation: 𝜕𝑡𝑢−𝜕5𝑥𝑢−10𝜕𝑥(𝑢3)+10𝜕𝑥(𝜕𝑥𝑢)2=0, 𝑡,𝑥∈ℝ, 𝑢(0,𝑥)=𝜙(𝑥), 𝑥∈ℝ. This equation is obtained by removing the nonlinear term 10𝑢𝜕3𝑥𝑢 from the fifth-order KdV equation. We show the existence of the local solution which is real...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2011/238138 |
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