Existence of solutions of the Cauchy problem using a fundamental solution
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I am looking for references on a general theory/results where a fundamental solution is used to show the existence of solutions for the Cauchy problem given some
Initial data.
To be more precise: let’s assume I am considering a second order parabolic differential equation on the whole Euclidean space $mathbb{R}^n$ with some in initial data $u_0$.
For the heat equation it is well known that on can construct solutions given some initial data using the fundamental solution.
I am looking for a reference where this process/method is carried out in a general setting.
reference-request pde fundamental-solution cauchy-problem
asked Dec 19 '18 at 17:21
LükLük
807
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add a comment |
$begingroup$
I am looking for references on a general theory/results where a fundamental solution is used to show the existence of solutions for the Cauchy problem given some
Initial data.
To be more precise: let’s assume I am considering a second order parabolic differential equation on the whole Euclidean space $mathbb{R}^n$ with some in initial data $u_0$.
For the heat equation it is well known that on can construct solutions given some initial data using the fundamental solution.
I am looking for a reference where this process/method is carried out in a general setting.
reference-request pde fundamental-solution cauchy-problem
asked Dec 19 '18 at 17:21
LükLük
807
$endgroup$
add a comment |
$begingroup$
I am looking for references on a general theory/results where a fundamental solution is used to show the existence of solutions for the Cauchy problem given some
Initial data.
To be more precise: let’s assume I am considering a second order parabolic differential equation on the whole Euclidean space $mathbb{R}^n$ with some in initial data $u_0$.
For the heat equation it is well known that on can construct solutions given some initial data using the fundamental solution.
I am looking for a reference where this process/method is carried out in a general setting.
reference-request pde fundamental-solution cauchy-problem
asked Dec 19 '18 at 17:21
LükLük
807
$endgroup$
I am looking for references on a general theory/results where a fundamental solution is used to show the existence of solutions for the Cauchy problem given some
Initial data.
To be more precise: let’s assume I am considering a second order parabolic differential equation on the whole Euclidean space $mathbb{R}^n$ with some in initial data $u_0$.
For the heat equation it is well known that on can construct solutions given some initial data using the fundamental solution.
I am looking for a reference where this process/method is carried out in a general setting.
reference-request pde fundamental-solution cauchy-problem
reference-request pde fundamental-solution cauchy-problem
asked Dec 19 '18 at 17:21
LükLük
807
asked Dec 19 '18 at 17:21
LükLük
807
asked Dec 19 '18 at 17:21
LükLük
807
asked Dec 19 '18 at 17:21
LükLük
807
asked Dec 19 '18 at 17:21
LükLük
807
807
add a comment |
add a comment |
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