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2 votes
0 answers
154 views

Uniqueness of the solution to systems of first-order linear PDEs

Context: Let ΩRp be an domain. For functions Aijk:ΩR and Bik:ΩR with some regularity, I am interested in the following ...
Paruru's user avatar
  • 51
3 votes
1 answer
243 views

Existence and uniqueness of solutions for continuous and directionally differentiable ODE

Given f:RnRn 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{...
Todd Chavez's user avatar
0 votes
0 answers
41 views

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 ...
fayez ahmed's user avatar
1 vote
0 answers
94 views

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{...
Eddy's user avatar
  • 111
2 votes
1 answer
155 views

Lotka Volterra existence of Caratheodory solution

I strive to prove that the following system of differential equations: {x=xu(t)xyy=y+u(t)xyx(0)=x0>0y(0)=y0>0 has a unique Caratheodory solution ...
Bogdan's user avatar
  • 1,759