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Results tagged with ap.analysis-of-pdes
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user 15946
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
0
votes
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answer
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Nonlinear PDE ${u_{tt}}^2u_{ttxx} = 1$
I have been trying to solve this equation during fortnight
$$
{u_{tt}}^2u_{ttxx} = 1.
$$
But I still here. The only thing is change of variables $u_{tt}(t,x) = y(t,x) $ and solved the ODE $y'' = \frac …
- 399
0
votes
If $t \to \lVert f(\cdot,t) \rVert_{L^2_x}^2$ is absolutely continuous, can we interchange t...
I will not assume function $$\psi(t) := \lVert f(\cdot,t) \rVert_{L^2_x}^2$$ be absolutely continuous.
We have $f\in W^{1,q'}_t\bigl([0,\infty), L^{p'}_x(S^1)\bigr)$, so $f$ has a representative $\til …
- 399