User riem

6 votes

2 answers

519 views

Existence of an integral equation (Faedo-Galerkin, Banach fixed point, Picard-Lindelof)

asked May 27, 2014 at 10:55

3 votes

1 answer

751 views

A distributional normal derivative for functions in $H^1(\Omega)$

asked Sep 27, 2014 at 14:13

2 votes

1 answer

3k views

A comparison principle for parabolic equation

asked Apr 16, 2014 at 16:24

1 vote

1 answer

191 views

Getting an a priori bound on a nonlinear gradient term in PDE; how to adapt trick from $L^2$ case to $H^{-1}$ case?

asked Apr 8, 2014 at 20:55

1 vote

1 answer

353 views

A question about PDE argument involving monotone convergence theorem and Sobolev space

asked Jul 7, 2014 at 17:25

1 vote

0 answers

70 views

Equivalence of two definitions of weak solution (subtlety with null sets)

asked Apr 14, 2015 at 17:43

0 votes

1 answer

789 views

Pointwise (in time) convergence in $H^{-1}$ implies pointwise weak convergence in $L^q$, why?

asked Jul 16, 2014 at 21:00

0 votes

1 answer

254 views

Want to show $\lim_{\epsilon \to 0}\frac{1}{\epsilon} \int_0^T \langle u_t(t), T_\epsilon(u(t)) \rangle = \int_\Omega |u(T)| - \int_\Omega |u(0)|$

asked Jun 23, 2014 at 10:23

0 votes

1 answer

272 views

Getting existence for $L^1$ data given existence for $L^\infty$ data and $L^1$ continuous dependence result

asked Jun 26, 2014 at 15:46

0 votes

0 answers

606 views

$b_n \rightharpoonup b$ in $L^q(Q) \forall q < \infty$, $b_n \to b$ in $C^0([0,T];H^{-1})$ implies $b_n(t) \rightharpoonup b(t)$ in $L^q(\Omega)$

asked Jun 29, 2014 at 22:11

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10 Questions

Existence of an integral equation (Faedo-Galerkin, Banach fixed point, Picard-Lindelof)

A distributional normal derivative for functions in $H^1(\Omega)$

A comparison principle for parabolic equation

Getting an a priori bound on a nonlinear gradient term in PDE; how to adapt trick from $L^2$ case to $H^{-1}$ case?

A question about PDE argument involving monotone convergence theorem and Sobolev space

Equivalence of two definitions of weak solution (subtlety with null sets)

Pointwise (in time) convergence in $H^{-1}$ implies pointwise weak convergence in $L^q$, why?

Want to show $\lim_{\epsilon \to 0}\frac{1}{\epsilon} \int_0^T \langle u_t(t), T_\epsilon(u(t)) \rangle = \int_\Omega |u(T)| - \int_\Omega |u(0)|$

Getting existence for $L^1$ data given existence for $L^\infty$ data and $L^1$ continuous dependence result

$b_n \rightharpoonup b$ in $L^q(Q) \forall q < \infty$, $b_n \to b$ in $C^0([0,T];H^{-1})$ implies $b_n(t) \rightharpoonup b(t)$ in $L^q(\Omega)$