<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      Questions tagged [linear-pde]

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

      5
      votes
      0answers
      210 views

      Research topics in Microlocal Analysis

      Before asking this question here I did some research on web but I would like to get the opinion of those directly interested if there are any , (as I did in this thread Research topics in distribution ...
      2
      votes
      1answer
      53 views

      Reference request: Schauder estimates for parabolic equations

      Where can I find Schauder estimates for second order linear parabolic equations (in divergence form with potential)? Any reference would be highly appreciated.
      6
      votes
      1answer
      92 views

      $W^{k,1}$ regularity for elliptic equations

      Let $\Omega$ be a bounded region in $\mathbb{R}^n$ and assume $u$ is a solutions of $\nabla \cdot (a \nabla u)=f$ with $a>c>0$ in $\Omega$, where $a\in C^k(\bar{\Omega})$. Is the following ...
      1
      vote
      0answers
      115 views

      6 linear PDE for only 3 unknowns?

      Let $x \in (0,L)$, $t \in (0,T)$, and let $u_0 = u_0(x) \in \mathbb{R}^3$, $g=g(t) \in \mathbb{R}^3$, $P = P(x,t) \in \mathbb{R}^3$ and $Q = Q(x,t) \in \mathbb{R}^3$ be continuously differentiable ...
      1
      vote
      1answer
      96 views

      First order partial differential equation [closed]

      I know there is a solution to this pde $$\partial_{t} f(t,x)= \partial_{x}(v(x)f(t,x))$$ $$ f(0,x)=g(x)$$ ( Where $v$ and $g$ are known functions) which is given by $$ f(t,x)=\frac{1}{v(x)} h(t+\...
      3
      votes
      1answer
      162 views

      Eigenfunctions of elliptic equations

      Let $\Omega$ be a bounded region in $\mathbb{R}^n$ and $a_1, a_2$ be smooth positive functions such that $a_1-a_2$ is compactly supported in $\Omega$, and $a_i>c>0$, for some constant $c$. ...
      1
      vote
      1answer
      58 views

      Global solutions of the wave equation with bounded initial condition

      Let $f,g$ be bounded compactly supported smooth functions, and assume $u$ is the solutions of the wave equation $$u_{tt}-c^2(x)\Delta u=0 \ \ \hbox{on} \ \ \mathbb{R}^n \times (0,\infty)$$ $$u(x,0)=f, ...
      1
      vote
      1answer
      88 views

      Two PDE for one unknown?

      Let $x \in (0,L)$, $t \in (0,T)$, and let $f_1 = f_1(x,t) \in \mathbb{R}$, $f_2 = f_2(x,t) \in \mathbb{R}$, $u^0 = u^0(x) \in \mathbb{R}$ and $g= g(t) \in \mathbb{R}$ be continuous functions. My ...
      0
      votes
      0answers
      24 views

      approach to perturb a linear operator

      My question is related to how one normally would perturb a linear operator. Let $B_1$ denote the open unit ball in $ R^N$ and suppose $\gamma>0$ is such that the operator $$L(\phi):=\Delta \phi(...
      2
      votes
      0answers
      24 views

      Wave equation regularity

      I have an equation of the type $$\hat{\rho} u_{tt}-\hat{E}u_{xx}=f(x,t)$$ for $x\in (0,1)$ and $t>0$, where $\hat{\rho}$ and $\hat{E}$ are constants, $u(0,t)=u(1,t)=0$, $u(x,0)=p(x)$, $u_t(x,0)=q(...
      0
      votes
      0answers
      90 views

      Harnack Inequality for uniformly elliptic PDE via constructing a singularity

      I am trying to prove a Harnack inequality for a nonnegative subsolution $u \in H^1(B_2)$ to the PDE $\text{div}(A Du) \ge 0$, where $A = A(x)$ is uniformly elliptic. The proof outline I am following ...
      1
      vote
      0answers
      153 views

      Replacing the initial conditions for a PDE

      The problem The PDE I am working with is given by $\left(\partial_a^b \leftrightarrow\frac{\partial^b}{\partial a^b}\right)$ $$\partial_t \psi = i \partial_x^2 \psi$$ $$\psi(x,t=0) = \psi_0(x)$$ $$\...
      1
      vote
      1answer
      49 views

      Exact solution of two coupled transport equations

      I want to solve the following system $$\eqalign{ & y_t = -y_x + z\text{ in }(0,\text{T}) \times (0,1) \cr & z_t = z_x + y\text{ in }(0,\text{T}) \times (0,1) \cr & y(0,x) = y_0,\,\,z(...
      5
      votes
      3answers
      393 views

      fundamental solution of an elliptic PDE in divergence form with non-symmetric matrix

      I am looking for the fundamental solution of the following PDE $$\partial_i (a^{ij}\partial_j u)=f$$ where $a^{ij}(x)$ is a non-symmetric matrix with possibly non-constant coefficients. I could ...
      4
      votes
      1answer
      243 views

      Existence of solution for the PDE $p \frac{\partial f(p, q)}{\partial p}-q \frac{\partial f(p, q)}{\partial q}=g(p, q)$

      Consider the following PDE: \begin{equation} p \frac{\partial f(p, q)}{\partial p}-q \frac{\partial f(p, q)}{\partial q}=g(p, q),\tag{$\star$} \end{equation} where $g$ is a flat function at the point (...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>