Question

Can smooth ODE converge to its equilibrium in finite time?

score 430 · Answer 1 · 2026-04-09 08:06:56

430

Views

Can smooth ODE converge to its equilibrium in finite time?

Published on 09 Apr 2026 - 8:06

score 640 · Answer 2 · 2026-04-09 08:09:23

640

Views

Closed-form solutions to $x''+\frac{k}{m}\ x+\mu\ g\ \text{sgn}(x')=0$

Published on 09 Apr 2026 - 8:09

score 338 · Answer 3 · 2026-04-09 08:06:57

338

Views

Solving $x''+x+\text{sgn}(x')\sqrt{|x'|} = 0\ $ Does it have closed form solutions? Does it stop moving? Could it stop at a different place than zero?

Published on 09 Apr 2026 - 8:06

score 152 · Answer 4 · 2026-04-09 10:08:06

152

Views

Solving $x'=-\text{sgn}(x)\sqrt{|x|}$: Uniqueness of solutions of finite duration

Published on 09 Apr 2026 - 10:08

score 118 · Answer 5 · 2026-04-09 08:05:29

118

Views

How to force my differential equations give a bounded solution?

Published on 09 Apr 2026 - 8:05

score 584 · Answer 6 · 2026-04-09 10:04:01

584

Views

Laplace transform region of Convergence of a finite duration signal

Published on 09 Apr 2026 - 10:04

score 152 · Answer 7 · 2026-04-09 10:05:41

152

Views

It is possible for a scalar finite-duration continuous system to achieve an infinite speed (in finite-time)? How if true? Why not if false?

Published on 09 Apr 2026 - 10:05

score 51 · Answer 8 · 2026-04-09 08:05:54

51

Views

Could non-smooth time-limited functions been Analytical?

Published on 09 Apr 2026 - 8:05

score 57 · Answer 9 · 2026-04-09 10:06:31

57

Views

Are there any continuous time-limited Linear and Time-Invariant (LIT) functions with unbounded derivative?

Published on 09 Apr 2026 - 10:06

score 125 · Answer 10 · 2026-04-09 08:06:55

125

Views

Could a continuous time-limited and absolute integrable function be the output of a causal continuous-time LTI system (Linear and Time-Invariant)??

Published on 09 Apr 2026 - 8:06

score 69 · Answer 11 · 2026-04-09 08:09:51

69

Views

For finite-duration continuous $f(t)$ with $\|f'(t)\|_\infty < \infty$: It is true $\|f'(t)\|_\infty \leq \frac{2\pi \|f'(t)\|_2^2}{\|f'(t)\|_1}$?

Published on 09 Apr 2026 - 8:09

score 71 · Answer 12 · 2026-04-09 08:06:31

71

Views

It is possible to (continuous-time) finite-duration continuous systems to be linear?

Published on 09 Apr 2026 - 8:06

score 109 · Answer 13 · 2026-04-09 08:10:53

109

Views

Non-smooth continuous and compact-supported 1-D functions with Fourier transform: Could they be defined through differential equations? Any examples?

Published on 09 Apr 2026 - 8:10

score 194 · Answer 14 · 2026-04-09 08:06:48

194

Views

It is possible for a (electromagnetic) wave equation to have as a solution a finite-duration/compact-supported function? Any closed-form examples?

Published on 09 Apr 2026 - 8:06

score 303 · Answer 15 · 2026-04-09 08:09:51

303

Views

It is possible to find a solution to $y''+\sqrt{|y|}\operatorname{sgn}(y)+\sqrt{|y'|}\operatorname{sgn}(y')=0,$ $\,y'(0)=0,\,y(0)= 1/4$?

Published on 09 Apr 2026 - 8:09

List Question

Can smooth ODE converge to its equilibrium in finite time?

Closed-form solutions to $x''+\frac{k}{m}\ x+\mu\ g\ \text{sgn}(x')=0$

Solving $x''+x+\text{sgn}(x')\sqrt{|x'|} = 0\ $ Does it have closed form solutions? Does it stop moving? Could it stop at a different place than zero?

Solving $x'=-\text{sgn}(x)\sqrt{|x|}$: Uniqueness of solutions of finite duration

How to force my differential equations give a bounded solution?

Laplace transform region of Convergence of a finite duration signal

It is possible for a scalar finite-duration continuous system to achieve an infinite speed (in finite-time)? How if true? Why not if false?

Could non-smooth time-limited functions been Analytical?

Are there any continuous time-limited Linear and Time-Invariant (LIT) functions with unbounded derivative?

Could a continuous time-limited and absolute integrable function be the output of a causal continuous-time LTI system (Linear and Time-Invariant)??

For finite-duration continuous $f(t)$ with $\|f'(t)\|_\infty < \infty$: It is true $\|f'(t)\|_\infty \leq \frac{2\pi \|f'(t)\|_2^2}{\|f'(t)\|_1}$?

It is possible to (continuous-time) finite-duration continuous systems to be linear?

Non-smooth continuous and compact-supported 1-D functions with Fourier transform: Could they be defined through differential equations? Any examples?

It is possible for a (electromagnetic) wave equation to have as a solution a finite-duration/compact-supported function? Any closed-form examples?

It is possible to find a solution to $y''+\sqrt{|y|}\operatorname{sgn}(y)+\sqrt{|y'|}\operatorname{sgn}(y')=0,$ $\,y'(0)=0,\,y(0)= 1/4$?

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