Hopf-Cole transformation to some systems of partial differential equations
| Autor: | A. S. Vasudeva Murthy, K. T. Joseph |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Stochastic partial differential equation
Elliptic partial differential equation Applied Mathematics Mathematical analysis First-order partial differential equation Exponential integrator Parabolic partial differential equation Hyperbolic partial differential equation Analysis Separable partial differential equation Numerical partial differential equations Mathematics |
| Zdroj: | Nonlinear Differential Equations and Applications. 8:173-193 |
| ISSN: | 1021-9722 |
| DOI: | 10.1007/pl00001444 |
| Popis: | In this paper we study a system of nonlinear partial differential equations which we write as a Burgers equation for matrix and use the Hopf-Cole transformation to linearize it. Using this method we solve initial value problem and initial boundary value problems for some systems of parabolic partial differential equations. Also we study an initial value problem for a system of nonlinear partial differential equations of first order which does not have solution in the standard distribution sense and construct an explicit solution in the algebra of generalized functions of Colombeau. |
| Databáze: | OpenAIRE |
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