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Results tagged with parabolic-pde
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user 60869
Questions about partial differential equations of parabolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
1
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0
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Regularity of solutions to $u' + Au = f$ for nonlinear monotone operator $A$
Consider the equation
$$u' + Au = f$$
$$u|_{\partial \Omega} = 0$$
$$u(0) = u_0$$
where $A:L^p(0,T;W^{1,p}_0) \to L^q(0,T;W^{-1,q})$ is some monotone nonlinear operator (with additional assumptions). …
- 93
3
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0
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Existence of solution to weak form of linear equation with boundary integral (parabolic PDE)
Let $W(0,T) := \{ u \in L^2(0,T;H^{\frac 12}(\partial\Omega)) \mid u_t \in L^2(0,T;H^{-\frac{1}{2}}(\partial\Omega))\}$. Let $\gamma$ and $\xi$ denote the trace map and its right inverse.
Does there …
- 93