query: Smoothness of the solutions of the Cauchy problem for quasi linear pde (Burgers' equation)
positive_passages.docid: 20837
positive_passages.text: Which of the choices solution of the Cauchy problem?
negative_passages.docid: 28888
negative_passages.text: The functional $I[w] = \int_U \frac{1}{2} |Dw|^2 - fw \, dx$ is weakly lower semicontinuous
negative_passages.docid: 62211
negative_passages.text: Partial Differential Equation $U_t - (U_x)^2 = 0$
negative_passages.docid: 93806
negative_passages.text: $\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
negative_passages.docid: 59370
negative_passages.text: Weak solutions to the Neumann's problem (Evans PDE)
negative_passages.docid: 893
negative_passages.text: Simple PDE with Neumann BC
negative_passages.docid: 2952
negative_passages.text: Cauchy-Riemann equations in polar form.
negative_passages.docid: 142436
negative_passages.text: Solving a PDE with variable coefficients
negative_passages.docid: 69945
negative_passages.text: A PDE exercise from Gilbarg Trudinger. problem 2.2
negative_passages.docid: 14656
negative_passages.text: The differential equation $xu_{x}+yu_{y}=2u$ satisfying the initial condition $y=xg(x),u=f(x)$
negative_passages.docid: 120170
negative_passages.text: A late-diverging "approximating solution" for a system of functional equations
negative_passages.docid: 125026
negative_passages.text: When does order of partial derivatives matter?
negative_passages.docid: 115033
negative_passages.text: Find the solution of the pde $xu_y-yu_x=u$.
negative_passages.docid: 140666
negative_passages.text: Solving the Quasilinear PDE $u_{t} - u^2 u_{x} = 0$ with piecewise initial condition.
negative_passages.docid: 52620
negative_passages.text: Solve the pde $u_t(x,t)=u_{xx}(x,t)-bu(x,t)+q(t)$ for $u(x,t)$
negative_passages.docid: 51546
negative_passages.text: Geometrical Interpertation of Cauchy's Mean Value Theorem
negative_passages.docid: 133471
negative_passages.text: Solve a PDE on a domain $\Omega$ with given boundary conditions