All Questions
Tagged with ap.analysis-of-pdes differential-equations
260 questions
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Non linear second order PDE involving max operator (Dynamic Programming)
I'm trying to solve the following Dynamic Programming equation in continuous time ($dt \rightarrow 0$)
$$ v(x,t) = \max\Big\{|x|\,,\,v(x,t)+dt\Big(v_t(x,t)+\frac{1}{2(t+1)}v_{xx}(x,t)\Big) \Big\} - \...
- 109
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47
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what classical PDEs have analytical expressions for soliton-like shape solutions but motionless?
what classical PDEs have analytical expressions for soliton-like shape solutions but motionless?
for example, KdV has analytical expressions of the kind (sech^2(x-vt)), but all of them are ...
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208
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3D Homogenous Laplace equation with integral boundary conditions
I have the 3D Laplace equation:
$$\nabla^{2} T_w = 0$$
where $\nabla^{2}=(\frac{\partial^{2}}{\partial x^2}+\frac{\partial^{2}}{\partial y^2}+\frac{\partial^{2}}{\partial z^2})$ defined on $x \in [0,...
- 47
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118
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Biharmonic equation
Let us consider for $0<\alpha\leq V(x)\leq \beta$ and $0\leq K(x)<\gamma$ the equation
\begin{equation}\label{\star}
\Delta^2u+V(x)u=g(x, u)+K(x)u,
\end{equation}
where $|g(x,s)|\leq \varepsilon|...
- 69
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94
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existence of an initial-boundary value problem with nonhomogeneous boundary conditions
Let $n\geq 2$ be an integer and $\Omega\in R^n$ be a bounded domain with boundary $\partial\Omega$ . Consider the following IBVP:
$u_t=\Delta u$, for $x\in \Omega$, $t>0$;
$u(x, 0)=f(x), x\in\...
- 103
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405
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Isothermal coordinates
Is there an application or interest in studying the isothermal surfaces where the metric is $ds^2=E∗(du^2+dv^2)$ and where $E>0$ is an harmonic function?
I know that this metric is a special kind ...
- 272
-1
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1
answer
127
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Solving a fully nonlinear first order PDE
given a symmetric matrix of Holder continuous functions $A(x)$ such that
$$
\frac{1}{C} |\xi|^2 \leq \langle A(x)\xi,\xi \rangle \leq C |\xi|^2
$$
find a vector field $\Phi$ such that
$$
D \Phi(x)^t D ...
- 261
-1
votes
1
answer
136
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An elementary question about integration by parts! [closed]
Let $f,g: R \rightarrow R$ be two positive increasing functions. Under what (non-trivial) conditions one can guarantee that $\int_{0}^{\infty}f'g dx\geq \int_{0}^{\infty}g'fdx$.
-2
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1
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579
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General solution to ODE [closed]
Considering the following ODE : find $f(x)$ such that
$$\frac{\sigma^{2}}{2}\frac{d^2}{dx^2}f(x)+a(b-x)\frac{d}{dx}f(x)-(\rho+\lambda)f(x)=-\lambda g(x) $$
Where, $a,b,\rho,\lambda,\sigma\in(0,+\...
- 29
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1
answer
872
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Existence and uniqueness of solutions for a system of first order PDEs [closed]
Which results can be applied and which conditions are needed, to ensure the existence and uniqueness of the solutions of the first order of PDEs:
A$\dfrac{\partial}{\partial t}\pmb{v}(t,x)=B(t,x,\pmb{...
- 103