Questions about partial differential equations of parabolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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### Approximation in parabolic Sobolev spaces

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### How to solve this linear Cauchy Problem

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### Steklov averages and negative parabolic sobolev spaces

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### For what functions does Nash inequality becomes equality?

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### Decay estimate for the heat equation: $\sup_{t>0}\int_{\mathbb{R}} t^\alpha |u_x|^2\ dx$

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### A question about whether an operator can be lipschitz or not

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### Isometries along the normalized Ricci flow

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### Classification of a system of two second order PDEs with two dependent and two independent variables

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### Boundary controllability of the heat equation and observation

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### Curvature decay of Ricci expanders

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### Classical solution of one dimensional Parabolic equation and a priori estimates

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### Heat equation, free boundary and dynamic programming

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### Reference request: Existence/regularity for viscous Hamilton-Jacobi equations

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### Observability inequality for the heat equation

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### Existence (linear) parabolic second order system in non-divergence form

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### Reference request for Vanishing viscosity method paper

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### Backward heat equation [closed]

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### Vanishing viscosity limits in PDEs and random functions

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### $L^p$-norm under the heat flow

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### Functional decaying under the heat flow (?)

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### Rate convergence of the heat equation as diffusion tends to zero

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### Reference for De Giorgi-Nash-Moser theory

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### schauder regularity heat equation

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### Hölder continuity of weak subsolutions to parabolic equations

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### Vorticity equation for generalized Naiver Stokes equations

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### Estimate of $\|\nabla u\|_{L^{\infty}(\mathbb R^2)}$ for incompressible Navier-Stokes equations

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### Parabolic (heat) PDE Green's function spatial asymptote at infinity

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### Critical spaces and energy estimate in NS equation [closed]

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### Relationships between fractional Sobolev space, Bessel spacse and Hajłasz–Sobolev space

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### Inhomogeneous heat kernel estimates

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### Solving parabolic PDE with Feynman-Kac but without Markov

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### Expected properties for a PDE whose solution is supposed to be something that doesn't exist

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### Reference request: $|\partial_t u - \Delta u|\in L^p(\Omega^T)$ implies Holder estimate

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### Linear PDE with non constant coefficients and properties of Green's Function

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### Parabolic Regularity with Neumann B.C

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### Looser condition for regularity for Neumann problems

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### Injectivity of a Fredholm operator

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### Looking for access to McKean's original paper?

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### Reference request : maximal regularity for the heat equation on the torus

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### Movement of a random walk in the limit (a particle in diffusion)

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### Motivation behind the parabolic metric

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### Green's functions/fundamental solution to a non-constant coefficients pde

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### Differentiable dependence on the data for parabolic equations

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### One-dimensional harmonic map flow with low regularity

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### Generator of spacetime Markov Process is Parabolic?

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### Classical solutions for parabolic PDE's

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### Regular Approximation for Degenerate Parabolic PDE

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### Mild solution of 2D surface quasi-geostrophic (SQG) equation

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### Infinitesimal generator of a semigroup with parameter

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