On the Unique Solvability of a Nonlinear Reaction-Diffusion Model with Convection
Copyright policy )On the Unique Solvability of a Nonlinear Reaction-Diffusion Model with Convection
The main goal of this article is to establish the uniqueness and comparison results for the nonnegative solution to the Cauchy-Dirichlet problem \[ u= u_0\quad\text{on}\quad\overline{\Omega}\times\{0\}; \quad u =\psi \quad \text{on}\quad \partial\Omega \] for the reaction-diffusion-convection equation \[ u_t = \Delta\varphi (x, t, u) + \nabla \cdot G(x, t, u) + f(x, t, u). \] The main approach is the Perron method using a priori estimates.
- Winona State University United States
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, maximal solution, Applied Mathematics, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Perron method, Cauchy-Dirichlet problem, A priori estimates in context of PDEs, Analysis
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, maximal solution, Applied Mathematics, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Perron method, Cauchy-Dirichlet problem, A priori estimates in context of PDEs, Analysis
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