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In terms of u the above first order PDE is the well-known Wave equation ... Initial value problem for the quasi-linear PDE (2.6) is a special Cauchy problem ...
In this video lecture, we discuss the Cauchy problem for first-order partial differential equation.This video is very helpful for students of BSc(Maths), B.T...
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface ...
In this video lecture, we discuss the Cauchy problem for first-order partial differential equation.This video is very helpful for students of BSc(Maths), B.T...
In Section 2 we establish the existence and uniqueness of a bounded solution u of (1.6), (1.4), and derive an a priori bound on its first ^-derivatives; this.
In the previous sections, we studied the method of characteristics for the solution of first and second order linear PDEs. We found that, normally, ...
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Solution of a PDE contains arbitrary elements. For a rst order PDE, it is an arbitrary function. In applications - additional condition )Cauchy problem. A Model Lession FD PDE Part 1 P. Prasad Department of Mathematics 16 / 50
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The Cauchy Problem for First Order Partial Differential Equations AYNER FRIEDMAN Communicated by Eberhard Hopf 1. Introduction. The Cauchy problem for quasi-linear equations <1.1) U, + X, u) + x, u) = 0 (0 < t ^ T), t-l OXi with initial data on t = 0, has been treated by many authors following the work of E. Hopf [9] who studied the special ...
The Cauchy Problem for First Order Partial Differential Equations AYNER FRIEDMAN Communicated by Eberhard Hopf 1. Introduction. The Cauchy problem for quasi-linear equations <1.1) U, + X, u) + x, u) = 0 (0 < t ^ T), t-l OXi with initial data on t = 0, has been treated by many authors following the work of E. Hopf [9] who studied the special ...
1.4 Cauchy problem A PDE in any area of application is always encountered with some auxiliary condi-tions. For a rst order PDE this condition can be formulated in the form of a Cauchy problem, which we state in a simple language below. Consider a curve in (x;y)-plane given by: x= x 0( ); y= y 0( ); 2IˆR; (1.6) where Iis an interval of the real ...
A similar problem in studying a partial differential equation of the first order with two independent variables is the problem of finding an integral surface ...