Qualitative properties of solutions to semilinear heat equations (Q1082539)
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scientific article; zbMATH DE number 3973437
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Qualitative properties of solutions to semilinear heat equations |
scientific article; zbMATH DE number 3973437 |
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Qualitative properties of solutions to semilinear heat equations (English)
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1986
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The author reviews some new results for the equation \[ u_ t-\Delta u=f(u)\quad in\quad \Omega \times (0,T),\quad Bu(x,t)=0\quad on\quad \partial \Omega \times (0,T), \] \[ u(x,0)=u_ 0(x)\geq 0\quad in\quad \Omega \] and compares these results with results for corresponding homogeneous, elliptic and ordinary differential equations, respectively.
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semilinear heat equations
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smoothing properties
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contractivity
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Ljapunov functionals
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blow up
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symmetrization
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asymptotic behavior
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shape preservation
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