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4 questions
2
votes
1
answer
133
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Global first integral for certain $3$ dimensional system
A physicist colleague asks me the following question. I have no idea to answer him. Your answer is very appreciated.
Is there a global first integral on $\mathbb{R}^3$ for the following vector field?
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5
votes
1
answer
414
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Fredholm index vs. Limit cycle theory
Let $A$ be the algebra of all smooth functions $f: \mathbb{R}^2 \to \mathbb{R}$ such that $f$ is flat at the origin and is real analytic on $\mathbb{R}^2 \setminus \{0\}$.
Let $B $ be ...
CommunityBot
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-4
votes
1
answer
872
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Existence and uniqueness of solutions for a system of first order PDEs [closed]
Which results can be applied and which conditions are needed, to ensure the existence and uniqueness of the solutions of the first order of PDEs:
A$\dfrac{\partial}{\partial t}\pmb{v}(t,x)=B(t,x,\pmb{...
CommunityBot
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3
votes
2
answers
361
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Regularity of a nonlinear ODE [Traveling wave solutions of parabolic systems]
In the book of Volpert on Traveling wave solutions of Parabolic Systems (AMS), one reads "the following assertion is readily proved and we shall not discuss it in detail". The same result is tacitely ...
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