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

3 votes
0 answers
138 views

How to prove the existence of weak solutions of parabolic PDEs using Rothe's method?

I am reading a textbook on PDE (Introduction to Elliptic and Parabolic Partial Differential Equations by Z. Wu, J. Yin and C. Wang, written in Chinese) where a proof of the existence of weak solutions …
1 vote
0 answers
76 views

While doing Lp estimates, is the constant C monotonically increasing with respect to the par...

For example, consider the third boundary value problem: \begin{align} &\frac{\partial u}{\partial t}-\sum_{i,j=1}^n a_{ij}(x,t) \frac{\partial^2 u}{\partial x_i \partial x_j} + \sum_{i=1}^n b_i(x, …