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Results tagged with ap.analysis-of-pdes
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user 480000
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
Accepted
Conditions for the existence of a solution to a semilinear second-order PDE with a-priori bo...
After a lot of reading, I came across the (enlightening) paper:
On principally linear elliptic differential equations of the second order, Nagumo 1954.
Basically, the (classical) results there shows t …
- 91
4
votes
1
answer
329
views
Conditions for the existence of a solution to a semilinear second-order PDE with a-priori bo...
Consider the general semilinear elliptic second-order PDE
$$
u_t-\mathcal L u=f\left(t,x,u,\nabla u\right)
$$
where $\mathcal L$ is an elliptic linear operator (like minus the Laplace operator), $t \i …
- 91
3
votes
1
answer
349
views
Solution or existence for a second-order semilinear PDE
Consider the following PDE:$$0=u_t+u_{yy}+u_{xx}+(x-y)u_y+y^{-\frac{3}{2}}u^2+1,$$ with $t \in [0,T], $ and a terminal condition $u_T=-1$ for all $x$ and $y.$ The domain for $x$ and $y$ can be bounded …
- 91