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I am looking for some maximum principles and comparison results for parabolic equations. The most complete book I've found on this subject is: Murray Protter, Hans Weinberger - Maximum Principles in ...

Note 1: the following question has been post on Math Stackexchange here but receive no respond. So I post it here to get more attention. Note 2: This is my research problem, but the original problem ...

I want to study how some numerical schemes work on $2$-dimensional reaction-diffusion systems on rectangles with Neumann Boundary conditions and I search for a while for a problem of the form: $$\...

Setup I'm trying to find sufficient conditions for the existence of a viscosity solution to the following PDE, $$ f(t,s,z) + \partial_sf(t,s,z) \\ + \sum_{i=1}^{\infty} \left[ \partial_{z_i} f(t,s,z)...

Let $J^s = (I- \Delta)^{\frac{s}{2}}$ where $\Delta$ is the Laplacian, and $w(x,y) \in L^2(\mathbb{T}^2)$. During my study to the paper, https://arxiv.org/pdf/1809.02027.pdf, the author stated that $$\...