All Questions
Tagged with uniqueness-theorems existence-theorems
5 questions
2
votes
0
answers
154
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Uniqueness of the solution to systems of first-order linear PDEs
Context:
Let Ω⊂Rp be an domain.
For functions Aijk:Ω→R and Bik:Ω→R with some regularity, I am interested in the following ...
3
votes
1
answer
243
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Existence and uniqueness of solutions for continuous and directionally differentiable ODE
Given f:Rn→Rn continuous and directionally differentiable (i.e., such that the directional derivative of f exists for any direction) at a neighborhood N of $x_0\in\mathbb{...
0
votes
0
answers
41
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Existence and Uniqueness of lifting Hele-Shaw problem
I am researching for the existence and uniqueness of solutions for the equation in figure below
enter image description here
∇⋅u=˙b(t)b(t) in Ω(t)
The ...
1
vote
0
answers
94
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Reference request: existence/uniqueness of solutions to convection diffusion equations
I am looking for a reference wherein existence and uniqueness results are proven for a system of PDEs of the form
$$
\frac{\partial Q}{\partial t} + A \frac{\partial Q}{\partial x} = f(Q,x,t) + \frac{...
2
votes
1
answer
155
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Lotka Volterra existence of Caratheodory solution
I strive to prove that the following system of differential equations:
{x′=x−u(t)xyy′=−y+u(t)xyx(0)=x0>0y(0)=y0>0
has a unique Caratheodory solution ...