List questions from parabolic-pde

Published on 03 Dec 2023 - 15:14

26

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If $\partial_t u_n -\Delta u_n = f_n$ , $\partial_t u -\Delta u =f$ and $f_n \to f$ in $L_t^p L_x^q$, do we have $u_n \to u$ in $W^{1,p}_t L^q_x$?

Published on 06 Dec 2023 - 14:25

22

Views

How to find numerically $\int_{0}^{1} w \langle \mathbf{p}, \mathbf{p}'\rangle \ du$ such $\nabla^2 w=0$ without solving the PDE for $w$ first?

Published on 07 Dec 2023 - 19:03

32

Views

Reference request: fractional heat equation $\partial_t u=(-\Delta)^s u$ with $s>1$

Published on 26 Mar 2026 - 2:50

70

Views

Use of Poincaré Inequality in Parabolic Equations a Priori Estimates

Published on 26 Dec 2023 - 9:29

85

Views

Solving heat equation with Lax-Milgram theory

Published on 06 Jan 2024 - 9:09

14

Views

Well-posedness of parabolic differential equations with Robin boundary condition

Published on 12 Jan 2024 - 8:40

74

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Showing the integral of the solution to a heat equation is constant

Published on 01 Feb 2024 - 8:39

18

Views

Phase speed of backward-time, central-space scheme

Published on 03 Feb 2024 - 23:12

24

Views

Higher regularity for linear parabolic equation with time depndent coefficient

Published on 09 Feb 2024 - 12:56

23

Views

Odd extension on two-dimensional parabolic PDE with boundary conditions

Published on 24 Feb 2024 - 6:07

42

Views

Heat semigroup is self-adjoint

Published on 25 Feb 2024 - 10:32

24

Views

Spatial analyticity for solutions of linear parabolic PDEs

Published on 27 Feb 2024 - 22:12

22

Views

How do we show that on a parabolic Hölder space, the polynomial and Hölder seminorms are equivalent?

Published on 25 Mar 2026 - 20:20

55

Views

Is the solution of the stochastic heat equation a Gaussian process?

Published on 23 Feb 2026 - 8:39

List Question

Existence of solution to a parabolic bvp

If $\partial_t u_n -\Delta u_n = f_n$ , $\partial_t u -\Delta u =f$ and $f_n \to f$ in $L_t^p L_x^q$, do we have $u_n \to u$ in $W^{1,p}_t L^q_x$?

How to find numerically $\int_{0}^{1} w \langle \mathbf{p}, \mathbf{p}'\rangle \ du$ such $\nabla^2 w=0$ without solving the PDE for $w$ first?

Reference request: fractional heat equation $\partial_t u=(-\Delta)^s u$ with $s>1$

Use of Poincaré Inequality in Parabolic Equations a Priori Estimates

Solving heat equation with Lax-Milgram theory

Well-posedness of parabolic differential equations with Robin boundary condition

Showing the integral of the solution to a heat equation is constant

Phase speed of backward-time, central-space scheme

Higher regularity for linear parabolic equation with time depndent coefficient

Odd extension on two-dimensional parabolic PDE with boundary conditions

Heat semigroup is self-adjoint

Spatial analyticity for solutions of linear parabolic PDEs

How do we show that on a parabolic Hölder space, the polynomial and Hölder seminorms are equivalent?

Is the solution of the stochastic heat equation a Gaussian process?

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